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Thank you for your incredible support and donation... I'm proud to tell you we received FDA approval to begin a Human Clinical Trial evaluating the safety of Schwann cells in people with spinal cord injuries in both the acute and chronic settings!... This is the only FDA approved trial using this type of cellular therapy on people with spinal cord injuries in the entire world... This approval offers real hope and shows we are closer than ever to curing spinal paralysis... I would like to offer my sincere gratitude on behalf of The Buoniconti Fund to Cure Paralysis for your most generous gift.


text:
Schindler's list »
Keneally, Thomas.
Listen Alaska
IL: UG - BL: 8.6 - AR Pts: 25
2nd Floor- Adult Books
FIC KENEALLY T.
1992, c1982. 1st Touchstone ed. Simon and Schuster, 398 p. : ill. ; 22 cm. English
1993. Hoopla Abridged. Simon & Schuster Audio, 1 online resource (1 audio file (240 min.)) : digital. English
Winner of the Booker Prize
Winner of the Los Angeles Times Book Award for Fiction
Schindler's List is a remarkable work of fiction based on the true story of German industrialist and war profiteer, Oskar Schindler, who, confronted with the horror of the extermination camps, gambled his life and fortune to rescue 1,300 Jews from the gas chambers.
Working with the actual testimony of Schindler's Jews, Thomas Keneally artfully depicts the courage and shrewdness of an unlikely savior, a man who is a flawed mixture of hedonism and decency and who, in the presence of unutterable evil, transcends the limits of his own humanity.
Holocaust, Jewish (1939-1945)
Holocaust, Jewish (1939-1945) -- Fiction
Holocaust, Jewish (1939-1945) -- Poland -- Kraków -- Fiction
Righteous Gentiles in the Holocaust
Righteous Gentiles in the Holocaust -- Poland -- Kraków -- Fiction
Schindler, Oskar
Schindler, Oskar, -- 1908-1974 -- Fiction
World War, 1939-1945 -- Fiction
World War, 1939-1945 -- Jews -- Rescue -- Poland -- Kraków -- Fiction
Kingsley, Ben.
ceabbf26-dbbb-f7af-fc55-7bfb8b01b690
schindler s list
keneally thomas
available_at_addison
During the Holocaust at the German concentration camp near Plaszow, thousands of Jews lost their lives at the hands of the Nazis. More than a thousand others would have been counted among the dead if not for a womanizing, heavy drinking, German-Catholic industrialist and Nazi Party member named Oskar Schindler. One of the most remarkable narratives of the Holocaust, Schindler's List masterfully recreates the daring exploits of Schindler, who used his enormous fortune to build a factory near the concentration camp and saved the lives of over 1,300 Jews. An absorbing, suspenseful and moving account of Oskar Schindler's legacy of life, this is an unforgettable audio program.
ils:.b10252472 .i12203701 2nd Floor- Adult Books FIC KENEALLY T. 1 false false Check Shelf Sep 16, 2014 afic
hoopla:MWT11634747 Online Hoopla Collection Online Hoopla eAudiobook Audio Books 1 false true Hoopla https://www.hoopladigital.com/title/11634747?utm_source=MARC Available Online
ils:.b10252472 Book Books 1st Touchstone ed. English Simon and Schuster, 1992, c1982. 398 p. : ill. ; 22 cm.
hoopla:MWT11634747 eAudiobook Audio Books Abridged. English Simon & Schuster Audio, 1993. 1 online resource (1 audio file (240 min.)) : digital.
ils:.b10252472 .i12203701 On Shelf Check Shelf false true true false false true 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 20, 21
Listen Alaska|
Schindler's list / Thomas Keneally
Schindler's list [electronic resource] / Thomas Keneally

redpajama_set_name: RedPajamaCommonCrawl


This image was created with a Point & Shoot camera. The ISO is 125 and was exposed for 1/160 sec @ f/4.5.
Love the contrast in this one. The white-whites and the black-blacks...very nice. Also I like the vignette. Nice work!
Nice capture of the action and the title in the newspaper box. Great work. Excellent choice in B&W.
Great shot. You truly captured that moment.
Just want to say "Thanks" to Nancy, Janet and Ness. I do appreciate each and every comment that I receive. The feedback is important to my photography and receiving comments like these does make me feel good about what I do.
A perfect one Glenn, really. Just the right moment.


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Sundowns had to sacrifice both players to make space for new signings Jeremy Brockie, Gaston Sirino and the returning Ricardo Nascimento, who was not registered in the first half of the season because of an injury.
"We have reached an agreement to loan out our two foreigners, Zakri at Ajax and Hachi at Chippa. We have kept Bangaly [Soumahoro], Ricardo came on and we still have [Razak] Brimah. So that's the foreign quota we have," Mosimane said today.
The decision to loan out Hachi meant Sundowns needed to get cover at left-back for Tebogo Langerman, which is why they signed Siyabonga Zulu from Platinum Stars.
"We needed cover. Zulu has played for Bafana Bafana. He did not have a good start [Zulu got a red card against Mauritania], but he has played for Bafana. He's got potential, so he is in the right space. If he does well, then he can get a chance," said Mosimane, before explaining why Hachi struggled to get game-time.
"Fares did not struggle so much. Offensively he has an edge on Langa [Langerman], but defensively Langa comes out quicker with the speed because we play with the fullbacks that go out, so Langa ticked that box. Sometimes it takes time for a player to adjust. It took Leo a lot of time. It took Sibusiso Vilakazi a year to get there.


text:
Ray T. Chen
The University of Texas,
Plenary Speaker of the Section
Rudolf Korsmik
State Marine Technical University, St.Petersburg, Russia
Mustafa Kansiz
Photothermal Spectroscopy Corp, USA
Manuela Pacella
Loughborough University, United Kingdom
Hendrik Swart
Natural and Agricultural Sciences, Republic of South Africa
Dear Esteemed Colleagues,
On behalf of the Organizing Committee, we are pleased to invite you to take part in the "5th International Conference on Photonics Research" which will be held on April 13-19, 2023 in the stunning Convention Centre of the Liberty Hotels Lykia /Oludeniz in Muğla, Turkey.
Interphotonics 2023 intends to be a global forum for researchers and engineers to present and discuss recent innovations and new techniques in Photonics Research. In addition to scientific seminars, a wide range of social programs including boat cruises and visits to historical places will be available.
The Organizing Committee also encourages companies and institutions to showcase their modern products and equipment in the conference area.
Further information is available on our conference website.
Specific questions concerning further information can be sent by e-mail to: chair@interphotonics.org
We are looking forward to meeting you at Interphotonics 2023
With our best regards,
Prof. Dr. Ersin Kayahan (Kocaeli University-LATARUM, Turkey)
Self-Accommodation
Self-accommodation option has been removed due to congress hotel concept.
All participants should stay in the congress hotel during their participation.
Please contact the congress secretariat (AİG TOUR) for accommodation reservations.
· Congress Secreteriat: reg@interphotonics.org
Abstract Book 2021
Abstract Book_2022
How to book your room from the venue or pay registration fees:
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2. Congress company will contact you with a proforma invoice (quotation)
3. In the invoice there will be multiple choices to pay. When your payment is received an e-mail will come to you confirming your payment.


text:
\section{Introduction}

Panel data models are useful to identify causal effects because they allow the researcher to control for multiple sources of unobserved heterogeneity modeled as individual and time effects. The general idea is to use variation across time to control for unobserved time invariant individual effects and to use contemporaneous variation across individuals to control for aggregate time effects. We consider estimation and inference on semiparametric nonlinear panel models with predetermined explanatory variables and interactive  individual and time effects. We focus on single index models, which cover  static and dynamic probit, logit, and Poisson models. We adopt a fixed effects approach that treats the realizations of the unobserved individual and time effects as parameters to be estimated, and therefore does not impose any restriction on the relationship between these effects and the observable explanatory variables.
Fixed effects estimation in nonlinear models with interactive effects, however, is computationally challenging and  suffers from the incidental parameter problem.

\medskip

Maximum likelihood estimation of standard single index models with cross section data is computationally tractable because the likelihood function is concave in all the model parameters. This computational tractability is preserved in panel models with additive individual and time effects, but it breaks down in panel models with interactive effects because the index is no longer linear in the individual and time effects.  Moreover, the principal components algorithm proposed by Bai~\cite*{Bai:2009p3321} for linear models with interactive effects cannot be applied to nonlinear models. We deal with this challenge by proposing an iterative two-step algorithm to compute the fixed effects conditional maximum likelihood estimator (FE-CMLE), where each step solves a concave optimization program.  The algorithm is based on the observation that the likelihood program is concave on the individual effects after fixing the time effects and vice versa. We show that the algorithm converges to a local maximum, as the likelihood function decreases at each step of the algorithm. In a simple model where the FE-CMLE can be obtained by principal components methods, the iterative algorithm finds the same estimates as principal components up to numerical tolerance error.

\medskip

We characterize the asymptotic properties of the FE-CMLE under sequences where the cross section ($N$) and time series ($T$) dimensions of the panel pass to infinity at the same rate. We give conditions for consistency of the estimators of the  index coefficients. Consistency is  hard to establish in this setting  because the dimension of the parameter space grows with the sample size and we cannot resort to concavity, unlike in models with additive individual and time effects. While consistent, the FE-CMLE has a bias in the asymptotic distribution  of the same order as the  variance. This is the large-$T$ version of the well-known incidental parameter problem \cite{Neyman:1948p881}, where the bias arises from the large number of estimated parameters and the nonlinearity of the model. We characterize the first order bias, and propose analytical and jackknife corrections that remove the bias from the asymptotic distribution. Asymptotically the correction does not increase variance and the confidence intervals constructed around the corrected estimator have correct coverage. We also derive asymptotic theory for fixed effects estimators of average partial effects (APEs). These APEs are often the quantities of interest in nonlinear models  and are functions of the data, index coefficients and unobserved individual and time effects. As Fernandez-Val and Weidner~\cite*{FW13}, we find that in general the incidental parameter bias is asymptotically of second order  because the estimators of the  APEs have  slower rate of convergence than the estimators of the index coefficients.
In numerical simulations, we show that the asymptotic results provide a good approximation to the behavior of the FE-CMLE and the bias corrections perform well in finite samples for multiple values of $N$ and $T.$

\paragraph{Literature review: } Neyman and
Scott \cite*{Neyman:1948p881}, Heckman \cite*{Heckman:1981p2940},
Lancaster \cite*{Lancaster:2000p879}, and Greene \cite*{Greene:2004p3125} discussed the incidental parameter problem in panel data models.  Phillips and Moon \cite*{Phillips:1999p733}, Hahn and Kuersteiner \cite*{Hahn:2002p717}, Lancaster \cite*{Lancaster:2002p875}, Woutersen~\cite*{Woutersen:2002p3683},
Hahn and Newey~\cite*{Hahn:2004p882},
Carro \cite*{Carro:2007p3601},
Arellano and Bonhomme~\cite*{ArellanoBonhomme2009},
Fernandez-Val~\cite*{FernandezVal:2009p3313},
Hahn and Kuersteiner~\cite*{HahnKuersteiner2011},
Fernandez-Val and Vella~\cite*{FernandezValVella2011},
and Kato, Galvao and Montes-Rojas~\cite*{KatoGalvaoMontes-Rojas2012} proposed large-$T$ bias corrections for fixed effects estimators in linear and nonlinear panel models with additive individual effects; see also Arellano and Hahn \cite*{ArellanoHahn2007} for a recent survey on this literature.   Bai~\cite*{Bai:2009p3321} and Moon and Weidner~\cite*{MoonWeidner2013a,MoonWeidner2013b}  considered large-$T$ bias corrections for FE-CMLE estimators of linear models with interactive individual and time effects.  Charbonneau \cite*{Charbonneau2011} and Fernandez-Val and Weidner~\cite*{FW13} considered fixed effects estimation of nonlinear panel models with additive individual and time effects.

\medskip

In Section \ref{sec:model}, we introduce the model and fixed effects estimators. Section  \ref{sec:bc}  describes the bias corrections to deal with the incidental parameters problem and illustrates how the bias corrections work through an example. Section  \ref{sec:app_panel} provides
 the asymptotic theory.  Section \ref{sec:numeric}  gives numerical examples. We collect the proofs of all the results and additional technical details in the Appendix.

\section{Model and Estimators}
\label{sec:model}

\subsection{Model} The data consist of $N \times T$ observations $\{(Y_{it}, X'_{it})': 1 \leq i \leq N, 1 \leq t \leq T \},$ for a scalar outcome variable of interest $Y_{it}$ and a vector
of explanatory variables $X_{it}$.  We assume that the outcome for
individual $i$ at time $t$ is generated by the sequential conditionally independent process:
\begin{equation*}
Y_{it}  \mid X^t_i, \alpha, \gamma, \beta   \sim f_{Y}(\cdot \mid X_{it}'\beta + \alpha_i \gamma_t), \ \ (i = 1,...,N; t = 1, ..., T),
\end{equation*}
where  $X^t_i = (X_{i1}, \ldots, X_{it}),$  $\alpha = (\alpha_1, \ldots, \alpha_N)$, $\gamma = (\gamma_1, \ldots, \gamma_T)$,
$f_{Y}$ is a known probability function, and $\beta$ is a finite dimensional parameter vector.

The variables $\alpha_i$ and $\gamma_t$ are unobserved individual and time effects that in economic applications capture individual heterogeneity and aggregate shocks, respectively.  The model is semiparametric because  we do not specify the distribution of these effects nor their relationship with the explanatory variables. The conditional distribution $f_{Y}$ represents the parametric part of the model.
The vector $X_{it}$ contains predetermined variables
 with respect to $Y_{it}$. Note that $X_{it}$ can include lags of $Y_{it}$ to accommodate dynamic models. The model is a single index model because the explanatory variables and unobserved effects  enter $f_Y$ through the index $ z_{it} := X_{it}'\beta + \alpha_i \gamma_t$ and is interactive because the individual and time effects enter the index $z_{it}$ multiplicatively as $\alpha_i \gamma_t = \alpha_i \times \gamma_t$.

We consider three running examples  throughout the analysis:
\begin{example}[Linear model]\label{example: linear} Let $Y_{it}$ be a continuous outcome. We can model the conditional distribution of $Y_{it}$ using the Gaussian linear model
\begin{equation*}
f_{Y}(y \mid X_{it}'\beta + \alpha_i \gamma_t) = \varphi((X_{it}'\beta+ \alpha_i  \gamma_t)/\sigma)/\sigma, \ \ y \in \mathbb{R},
\end{equation*}
where $\varphi$ is the density function of the standard normal and $\sigma$ is a positive scale parameter.
\end{example}

\begin{example}[Binary response model]\label{example: probit} Let $Y_{it}$ be a binary outcome and $F$ be a cumulative
distribution function of  the standard normal or logistic distribution. We can model the conditional distribution of $Y_{it}$ using the probit or logit model
\begin{equation*}
f_{Y}(y \mid X_{it}'\beta + \alpha_i \gamma_t) = F(X_{it}'\beta+ \alpha_i  \gamma_t)^y[1 - F(X_{it}'\beta+ \alpha_i  \gamma_t)]^{1-y}, \ \ y \in \{0,1\}.
\end{equation*}
\end{example}

\begin{example}[Count response model]\label{example: poisson} Let $Y_{it}$ be a non-negative interger-valued outcome, and $f(\cdot; \lambda)$ be the
probability mass function of a Poisson random variable with mean $\lambda > 0$. We can model the conditional distribution of $Y_{it}$ using the Poisson model
\begin{equation*}
f_{Y }(y \mid X_{it}'\beta + \alpha_i \gamma_t) = f(y;  \exp[X_{it}'\beta + \alpha_i   \gamma_t ]), \ \ y \in \{0, 1,  2, .... \}.
\end{equation*}
\end{example}

For estimation, we adopt a fixed effects approach treating the realization of the unobserved individual and time effects as parameters to be estimated. We collect all these effects in the vector $\phi_{NT} = (\alpha_1, ..., \alpha_N, \gamma_1, ..., \gamma_T)'$.  The model parameter  $\beta$ includes the index coefficients of interest, while the unobserved effects $\phi_{NT}$ are  treated as a nuisance parameter.
The true values of the parameters, denoted by $\beta^0$
and $\phi_{NT}^0 = ({\alpha^{0}_1}, ..., {\alpha^{0}_N}, {\gamma^{0}_1}, ..., {\gamma^{0}_T})'$, are the solution to the population fixed effects conditional maximum likelihood program
\begin{align}\label{population_prob}
& \max_{(\beta, \phi_{NT})   \in \mathbbm{R}^{\dim \beta + \dim \phi_{NT}}} \; \mathbb{E}_{\phi}[ \mathcal{L}_{NT}(\beta,\phi_{NT})],
\nonumber \\
&  \qquad \mathcal{L}_{NT}(\beta,\phi_{NT}) := (NT)^{-1/2} \sum_{i,t}  \log f_{Y}(Y_{it}  \mid X_{it}'\beta +  \alpha_i \gamma_t),
\end{align}
for every $N,T$, where $\mathbb{E}_{\phi}$ denotes the expectation with respect to
the distribution of the data conditional on the unobserved effects and initial conditions including strictly exogenous variables.  We need to impose a scale normalization on $\phi_{NT}^0$ because multiplying by a constant  to all $\alpha_i$, while
dividing by same constant to all $\gamma_t$,  does not change  $\alpha_{i}  \gamma_t$.
We normalize $\phi^0_{NT}$ to satisfy  $\sum_i [\alpha_i^0]^2 = \sum_t
[\gamma_t^0]^2$. Existence and uniqueness of the solution to the population problem up to the scale normalization will be
guaranteed by our assumptions in Section~\ref{sec:app_panel} below, including concavity
of the objective function in the index $X_{it}'\beta + \alpha_i \gamma_t$.
The pre-factor $(NT)^{-1/2}$ in $\mathcal{L}_{NT}(\beta,\phi_{NT})$ is just a convenient rescaling  for the asymptotic analysis.

Other quantities of interest involve averages over the data and unobserved effects
\begin{equation} \label{eq: meffs}
 \delta^0_{NT} =    \mathbb{E} [\Delta_{NT}(\beta^0, \phi^0_{NT})], \ \ \Delta_{NT}(\beta, \phi_{NT}) = (NT)^{-1} \sum_{i,t}   \Delta(Y_{it},X_{it}, \beta, \alpha_i \gamma_t),
\end{equation}
where  $\mathbb{E}$ denotes the expectation with respect to
the joint distribution of the data and the unobserved  effects, provided that the expectation exists. They are indexed by $N$ and $T$ because the marginal distribution of $\{(X_{it}, \alpha_i, \gamma_t)  : 1 \leq i \leq N, 1 \leq t \leq T\}$ can be heterogeneous across $i$ and/or $t$; see Section \ref{subsec:apes}. These averages
include scale parameters and other average partial effects (APEs), which are often the ultimate
quantities of interest in nonlinear models.
Some examples of partial effects are the following:

\medskip

\noindent  \textbf{Example \ref{example: linear}} (Linear model).  \textit{The variance $\sigma^2$ in the linear model can be expressed as an APE with
\begin{equation}\label{example: probit: meff1}
\Delta(Y_{it}, X_{it}, \beta, \alpha_i \gamma_t) =  (Y_{it} - X_{it}'\beta - \alpha_i \gamma_t)^2.
\end{equation}
}

\noindent  \textbf{Example \ref{example: probit}} (Binary response model).  \textit{If $X_{it,k}$, the $k$th element of $X_{it}$, is
binary, its partial effect on the conditional probability of $Y_{it}$ is
\begin{equation}\label{example: probit: meff1}
\Delta(Y_{it}, X_{it}, \beta, \alpha_i \gamma_t) =  F(\beta_k +
X_{it,-k}'\beta_{-k}  + \alpha_i  \gamma_t) -
F(X_{it,-k}'\beta_{-k} + \alpha_i   \gamma_t),
\end{equation}
where $\beta_k$ is the $k$th element of $\beta$, and $X_{it,-k}$ and $\beta_{-k}$ include all elements of $X_{it}$ and $\beta$ except for the $k$th element. If $X_{it,k}$ is continuous and $F$ is differentiable, the partial effect of $X_{it,k}$
on the conditional probability of $Y_{it}$ is
\begin{equation}\label{example: probit: meff2}
\Delta(Y_{it},X_{it}, \beta, \alpha_i \gamma_t) = \beta_k  \partial F(X_{it}'\beta +
\alpha_i \gamma_t),
\end{equation}
where $\partial F$ is the derivative of $F$.
}

\medskip

\noindent  \textbf{Example \ref{example: poisson}} (Count response model). \textit{If $X_{it,k}$, the $k$th element of $X_{it}$, is
binary, its partial effect on the conditional probability of $Y_{it}$ is
\begin{equation}\label{example: poisson: meff1}
\Delta(Y_{it}, X_{it}, \beta, \alpha_i \gamma_t) =  \exp(\beta_k +
X_{it,-k}'\beta_{-k}  + \alpha_i  \gamma_t) -
\exp(X_{it,-k}'\beta_{-k} + \alpha_i   \gamma_t),
\end{equation}
where $\beta_k$ is the $k$th element of $\beta$, and $X_{it,-k}$ and $\beta_{-k}$ include all elements of $X_{it}$ and $\beta$ except for the $k$th element. If $X_{it,k}$ is continuous, the partial effect of $X_{it,k}$
on the conditional expectation of $Y_{it}$ is
\begin{equation}\label{example: poisson: meff}
\Delta(Y_{it}, X_{it}, \beta, \alpha_i \gamma_t) = \beta_k
 \exp(X_{it}'\beta + \alpha_i   \gamma_t).
\end{equation}
}

\subsection{Fixed effects estimators}

The  sample analog of the program \eqref{population_prob} is
\begin{equation}
\max_{(\beta, \phi_{NT}) \in  \mathbbm{R}^{\dim \beta + \dim \phi_{NT}}} \;  {\cal L}_{NT}(\beta,\phi_{NT}).
   \label{LobjMAX}
\end{equation}
As in the population case, we shall impose conditions guaranteeing that the solutions to the previous programs
 exist  and are unique with probability approaching one as $N$ and $T$ become large, including the scale normalization on $\phi_{NT}$. The program~\eqref{LobjMAX} cannot be solved using standard optimization algorithms because it is not concave in $\phi_{NT}$ due to the multiplicative structure.  We propose an iterative two-step algorithm for the case where the log-likelihood is concave in the index $z_{it}$, where each step solves a concave maximization program.  The algorithm is based on the observation that the log-likelihood program is concave on the individual effects after fixing the time effects and vice versa.   To describe the algorithm it is convenient to separate $\phi_{NT} = (\alpha,\gamma)$, so that $ {\cal L}_{NT}(\beta,\phi_{NT}) =  {\cal L}_{NT}(\beta,\alpha,\gamma)$.

 \begin{algorithm}[IFE-CMLE] \label{algorithm:IFE-CMLE}
 \begin{enumerate}
 \item Iteration 0: find initial values  $(\widehat \beta^{(0)}, \widehat \alpha^{(0)}, \widehat \gamma^{(0)})$ solving
 $$
 \widehat \gamma^{(0)} \in \operatorname*{argmax}_{(\beta, \gamma) \in  \mathbbm{R}^{\dim \beta + T}} {\cal L}_{NT}(\beta,1_N,\gamma), \ \   (\widehat \beta^{(0)}, \widehat \alpha^{(0)}) \in \operatorname*{argmax}_{(\beta, \alpha) \in  \mathbbm{R}^{\dim \beta + N}} {\cal L}_{NT}(\beta,\alpha,\widehat \gamma^{(0)}),
 $$
 where $1_N$ is a $N$-vector of ones.
 \item Iteration $k$: update $(\widehat \beta^{(k-1)}, \widehat \alpha^{(k-1)}, \widehat \gamma^{(k-1)})$ in two steps  solving
 \begin{enumerate}
 \item[Step 1:]  $\widehat \gamma^{(k)} \in \operatorname*{argmax}_{\gamma \in  \mathbbm{R}^{T}} {\cal L}_{NT}(\widehat \beta^{(k-1)},\widehat \alpha^{(k-1)},\gamma),$
 \item[Step 2:] $(\widehat \beta^{(k)}, \widehat \alpha^{(k)}) \in \operatorname*{argmax}_{(\beta, \alpha) \in  \mathbbm{R}^{\dim \beta + N}} {\cal L}_{NT}(\beta,\alpha,\widehat \gamma^{(k)}).$
 \end{enumerate}
 \item Repeat 2 until convergence in $m$ iterations, e.g. when
 $$
  {\cal L}_{NT}(\widehat \beta^{(m)},\widehat \alpha^{(m)},\widehat \gamma^{(m)}) -  {\cal L}_{NT}(\widehat \beta^{(m-1)},\widehat \alpha^{(m-1)},\widehat \gamma^{(m-1)}) < \epsilon_{tol},
 $$
 where $\epsilon_{tol}$ is a tolerance level (e.g., $10^{-4}$).
 \item Final iteration: define the IFE-CMLE as
 $$
 \widehat \beta_{NT} = \widehat \beta^{(m)}, \ \ \widehat \phi_{NT} = (c \widehat \alpha^{(m)}, \widehat \gamma^{(m)}/c),
 $$
where $c^4 = \widehat \gamma^{(m)'} \widehat \gamma^{(m)}/  \widehat \alpha^{(m)'} \widehat \alpha^{(m)}$. The rescaling by $c$  imposes the scale normalization $\sum_i \widehat \alpha_i^2 = \sum_t
\widehat \gamma_t^2$ in $\widehat \phi_{NT}$.
 \end{enumerate}
 \end{algorithm}

 \begin{remark}[Convergence of IFE-MLE] If $z_{it} \mapsto \log f_{Y}(Y_{it}  \mid z_{it})$ is concave, then the  objective functions in each step $\gamma \mapsto  {\cal L}_{NT}(\beta,\alpha,\gamma)$ and $(\beta,\alpha) \mapsto  {\cal L}_{NT}(\beta,\alpha,\gamma)$ are also concave. Moreover, in view of the fact
 $$
 {\cal L}_{NT}(\widehat \beta^{(k-1)},\widehat \alpha^{(k-1)},\widehat \gamma^{(k-1)}) \leq {\cal L}_{NT}(\widehat \beta^{(k-1)},\widehat \alpha^{(k-1)},\widehat \gamma^{(k)}) \leq {\cal L}_{NT}(\widehat \beta^{(k)},\widehat \alpha^{(k)},\widehat \gamma^{(k)}),
 $$
 the convergence of the algorithm to a local maximum of the program~\eqref{LobjMAX} is guaranteed. We find that the speed of convergence is fast in simulations.
 \end{remark}

To analyze the statistical properties of the estimator of $\beta$ it is conceptually
convenient to solve the program~\eqref{LobjMAX} in two steps. First, we concentrate out the nuisance parameter $\phi_{NT}$. For
given $\beta$, we define the optimal $\widehat \phi_{NT}(\beta)$  as
\begin{equation}
   \widehat \phi_{NT}(\beta) = \operatorname*{argmax}_{\phi_{NT} \in \mathbbm{R}^{\dim \phi_{NT}}}
       \,  {\cal L}_{NT}(\beta,\,\phi_{NT}) \;.
   \label{DefEstPhi}
\end{equation}
The fixed effects estimators of $\beta^0$ and $\phi_{NT}^0$ are then
\begin{equation}
   \widehat \beta_{NT} \, = \,
      \operatorname*{argmax}_{\beta \in  \mathbbm{R}^{\dim \beta}} \; {\cal L}_{NT}(\beta,\widehat \phi_{NT}(\beta)) \;,
       \qquad
   \widehat \phi_{NT} \, = \, \widehat \phi_{NT}(\widehat \beta).
   \label{DefEst}
\end{equation}

Estimators of APEs can be
formed by plugging-in the estimators of the model parameters in the sample version of \eqref{eq: meffs}, i.e.
\begin{equation}
    \label{eq:ape}
\widehat \delta_{NT}  =  \Delta_{NT}(\widehat \beta, \widehat \phi_{NT}).
\end{equation}

\section{Incidental parameter problem and bias corrections} \label{sec:bc}

In this section we give a heuristic discussion of the main results, leaving the technical details to Section~\ref{sec:app_panel}.

\subsection{Incidental parameter problem}

Fixed effects estimators in nonlinear or dynamic models
suffer from the
incidental parameter problem (Neyman and Scott, 1948).
The individual and time effects are incidental parameters
that cause the estimators of the model parameters to be
inconsistent under asymptotic sequences where either $N$ or $T$ are fixed.
To describe the problem  let
\begin{equation}\label{eq:pop_program}
\overline{\beta}_{NT} := \operatorname*{argmax}_{\beta \in  \mathbbm{R}^{\dim \beta}}  \;
    \mathbb{E}_{\phi}\left[ {\cal L}_{NT}(\beta,\widehat \phi_{NT}(\beta)) \right].
\end{equation}
In general,  $\operatorname*{plim}_{N \to \infty} \overline{\beta}_{NT} \neq \beta^0$ and $\operatorname*{plim}_{T \to \infty} \overline{\beta}_{NT} \neq \beta^0$
because of the estimation
error in $\widehat \phi_{NT}(\beta)$ when one of the dimensions is fixed.
 If $\widehat \phi_{NT}(\beta)$ is
replaced by $\phi_{NT}(\beta) = \operatorname*{argmax}_{\phi_{NT} \in
\mathbbm{R}^{\dim \phi_{NT}}}
       \,  \mathbb{E}_{\phi}[ {{\cal L}}_{NT}(\beta,\,\phi_{NT})]$, then the resulting
   $\overline \beta_{NT} = \beta^0$.
We consider analytical and jackknife corrections for
the bias $\overline{\beta}_{NT} - \beta^0.$

\subsection{Bias Corrections}
Some expansions can be used to explain our corrections.
Under suitable sampling conditions, the bias is
small for large enough $N$ and $T$, i.e., $\operatorname*{plim}_{N,T \to \infty} \overline{\beta}_{NT} = \beta^0$.
For smooth likelihoods and under appropriate regularity conditions, as $N,T \to \infty$,
\begin{equation}\label{eq: expansion}
\overline{\beta}_{NT} = \beta^0 + \overline B_{\infty}^{\beta}/T
+ \overline D_{\infty}^{\beta} /N + o_P(T^{-1} \vee N^{-1}),
\end{equation}
for some $\overline B_{\infty}^{\beta}$ and $\overline D_{\infty}^{\beta}$ that we characterize in Theorem \ref{th:BothEffects},
where $a \vee b := \max(a,b)$.
 Unlike in nonlinear models without incidental parameters, the order of the bias is higher than the inverse of the sample size $(NT)^{-1}$ due to the slow rate of convergence of  $\widehat \phi_{NT}$. Note also that by the properties of the maximum likelihood estimator
$$
\sqrt{NT}(\widehat \beta_{NT} - \overline{\beta}_{NT}) \to_d \mathcal{N}(0, \overline V_{\infty}).
$$

Under asymptotic sequences where $N/T \to \kappa^2$ as $N,T \to \infty$, the fixed effects estimator is asymptotically
biased because
\begin{align}
\sqrt{NT}(\widehat \beta_{NT} - \beta^0) &= \sqrt{NT}(\widehat \beta_{NT} - \overline{\beta}_{NT}) + \sqrt{NT}(\overline B_{\infty}^{\beta}/T
+ \overline D_{\infty}^{\beta} /N + o_P(T^{-1} \vee N^{-1})) \nonumber \\
 &\to_d \mathcal{N}( \kappa \overline B_{\infty}^{\beta}
+ \kappa^{-1} \overline D_{\infty}^{\beta} , \overline V_{\infty}).
\label{eq:MainResult}
\end{align}
This is the large-$N$ large-$T$ version of the incidental parameters problem that invalidates any inference based on the asymptotic distribution. Relative to fixed effects estimators with only individual effects, the presence of time effects
introduces additional asymptotic bias through $ \overline D_{\infty}^{\beta}$.

The analytical bias correction consists of removing estimates of the leading terms of the bias from the fixed effect estimator
of $\beta^0$. Let $\widehat B_{NT}^{\beta}$ and $\widehat D_{NT}^{\beta}$ be estimators of $\overline B_{\infty}^{\beta}$ and $\overline D_{\infty}^{\beta}$, respectively. The bias corrected estimator can be formed as
\begin{equation*}\label{abc}
\widetilde{\beta}_{NT}^A = \widehat{\beta}_{NT} -  \widehat{B}_{NT}^{\beta}/T - \widehat D_{NT}^{\beta}/N.
\end{equation*}
If $N/T \to \kappa^2$,  $\widehat B_{NT}^{\beta} \to_P \overline B_{\infty}^{\beta}$, and $\widehat D_{NT}^{\beta} \to_P \overline D_{\infty}^{\beta},$ then
\begin{equation*}
\sqrt{NT}(\widetilde \beta_{NT}^A - \beta^0)
\to_d \mathcal{N}(0, \overline V_{\infty}).
\end{equation*}
The analytical correction therefore centers the asymptotic distribution at the true value of the parameter, without increasing asymptotic variance.

We consider a jackknife bias correction method
that does not require explicit estimation of the bias, but is
computationally more intensive.  This method is the double split panel jackknife (SPJ) correction of Fernandez-Val and Weidner~\cite*{FW13}, which extended the jackknife correction of Dhaene and Jochmans~\cite*{Dhaene:2010p650} to models with additive individual and time effects.
Alternative jackknife corrections based on the leave-one-observation-out panel jackknife (PJ) of Hahn and Newey \cite*{Hahn:2004p882}  and combinations of PJ and SPJ are also possible. We do not consider corrections based on PJ because they are theoretically justified by second-order expansions of $\overline{\beta}_{NT}$ that are beyond the scope of this paper.

To describe  the double SPJ correction, let
$\widetilde{\beta}_{N,T/2}$ be the average of the 2 split jackknife
estimators that leave out the first and second halves of the time
periods, and let $\widetilde{\beta}_{N/2,T}$ be the average of the 2 split jackknife
estimators that leave out half of the individuals.\footnote{When $T$ is odd we define $\widetilde{\beta}_{N,T/2}$ as the average of the 2 split jackknife
estimators that use overlapping subpanels with $t \leq (T+1)/2$ and $t \geq (T+1)/2$. We define $\widetilde{\beta}_{N/2,T}$ similarly when $N$ is odd.}
In choosing the cross sectional
division of the panel, one might want to take into account individual clustering structures to
preserve and account for cross sectional dependencies.
If there are no cross sectional dependencies,   $\widetilde{\beta}_{N/2,T}$ can
be constructed as the average
of the estimators obtained from all possible partitions of $N/2$ individuals to avoid ambiguity and arbitrariness in the choice of the division.\footnote{There are $P =  {N \choose 2}$ different cross sectional partitions with $N/2$ individuals. When $N$
is large, we can approximate the average over all possible partitions  by the average over $S \ll P$ randomly chosen partitions to speed up computation.}
The bias corrected estimator is
\begin{equation}\label{eq: jackknife2}
\widetilde{\beta}_{NT}^{J} = 3  \widehat \beta_{NT} - \widetilde{\beta}_{N,T/2} - \widetilde{\beta}_{N/2,T}.
\end{equation}
To give some intuition about how the corrections works, note that
\begin{equation*}
\widetilde{\beta}_{NT}^{J}  - \beta_0 =  (\widehat \beta_{NT} - \beta_0)  - (\widetilde{\beta}_{N,T/2} - \widehat \beta_{NT}) - (\widetilde{\beta}_{N/2,T} - \widehat \beta_{NT}),
\end{equation*}
where
 $ \widetilde{\beta}_{N,T/2} - \widehat \beta_{NT} = \overline B_{\infty}^{\beta}/T + o_P(T^{-1} \vee N^{-1})$ and  $\widetilde{\beta}_{N/2,T} - \widehat \beta_{NT} = \overline D_{\infty}^{\beta}/N + o_P(T^{-1} \vee N^{-1}).$ The time series split removes the bias term $\overline B_{\infty}^{\beta}$ and the cross sectional split removes the bias term $\overline D_{\infty}^{\beta}.$

\section{Asymptotic Theory for Bias Corrections}
\label{sec:app_panel}

In nonlinear panel data models the population problem (\ref{eq:pop_program}) generally does not have closed form solution, so we need to
rely on asymptotic arguments to characterize the terms in the expansion of the bias (\ref{eq: expansion}) and to justify the validity of the corrections.

\subsection{Asymptotic distribution of model parameters}
We consider single index panel models with predetermined explanatory variables and scalar interactive individual and time effects that enter the likelihood function through  $z_{it} = X_{it}'\beta + \alpha_i  \gamma_t$. In these models the dimension of the incidental parameters is $\dim \phi_{NT} = N+T$.  These models cover  the
linear, probit and Poisson specifications of Examples~\ref{example: linear}--\ref{example: poisson}.
The parametric part of our panel models  takes the form
\begin{equation}\label{eq: index_model}
   \log f_{Y}(Y_{it} \mid X_{it}, \alpha_i, \gamma_t, \beta)
      = \ell_{it}(z_{it} ).
\end{equation}
We denote  the derivatives  of the log-likelihood function $\ell_{it}$ by $\partial_{z^q} \ell_{it}(z) := \partial^q \ell_{it}(z)/\partial z^q$, $q = 1,2, \ldots$
We drop the argument $z_{it}$ when the derivatives are evaluated at the true value of the index  $z^0_{it} := X_{it}'\beta^0 + \alpha_i^0  \gamma_t^0$, i.e.,
$\partial_{z^q} \ell_{it} := \partial_{z^q}\ell_{it}(z^0_{it})$. We also drop the dependence on
$NT$ from all the sequences of functions and parameters, e.g. we use $\mathcal{L}$ for $\mathcal{L}_{NT}$ and $\phi$
for $\phi_{NT}$.

We make the following assumptions:

\begin{assumption}[Panel models]
   Let $\nu > 0$ and $\mu>4 (8+\nu)/\nu$.
   Let $\varepsilon>0$ and let
     ${\cal B}^0_{\varepsilon}$ be a bounded subset of $\mathbbm{R}$
     that contains an $\varepsilon$-neighbourhood of $z^0_{it}$
     for all $i,t,N,T$.

   \label{ass:PanelA1}
   \begin{itemize}
      \item[(i)] Asymptotics: we consider limits of sequences where  $N/T \rightarrow \kappa^2$, $0<\kappa<\infty$, as $N,T \rightarrow \infty$.

      \item[(ii)] Sampling:  conditional on $\phi$, $\{(Y_i^T, X_i^T) : 1 \leq i \leq N \}$ is independent across $i$
          and, for each $i$, $\{ (Y_{it}, X_{it}) : 1 \leq t \leq T\}$ is $\alpha$-mixing with mixing coefficients
          satisfying $\sup_i a_i(m) = {\cal O}( m^{-\mu} )$ as $m \rightarrow \infty$, where
\begin{equation*}
 a_i(m) := \sup_t \sup_{A \in \mathcal{A}_{t}^i, B \in \mathcal{B}_{t+m}^i} |P(A \cap B) - P(A) P(B)|,
 \end{equation*}
and for $Z_{it} = (Y_{it}, X_{it})$,  $\mathcal{A}_{t}^i$ is the sigma field generated by $(Z_{it}, Z_{i,t-1}, \ldots)$, and
 $\mathcal{B}_{t}^i$ is the sigma field generated by $(Z_{it}, Z_{i,t+1}, \ldots)$.

     \item[(iii)] Model: for $X^t_i = \{X_{is}:  s = 1, ..., t\}$, we assume that for all $i,t,N,T,$
\begin{equation*}
Y_{it}  \mid X^t_i, \phi, \beta   \sim \exp[\ell_{it}( X_{it}'\beta + \alpha_{i}  \gamma_t)].
\end{equation*}
The realizations of the parameters and unobserved effects that generate the observed data are denoted by
$\beta^0$ and $\phi^0$.\

      \item[(iv)]  Smoothness and moments:
      We assume that
      $z \mapsto \ell_{it}(z)$ is
      four times continuously differentiable over ${\cal B}^0_{\varepsilon}$ a.s.
      The partial derivatives of  $\ell_{it}(z)$
      with  respect to  $z$
      up to fourth order
      are bounded in absolute value uniformly over $z \in {\cal B}^0_{\varepsilon}$
      by a function $M(Z_{it})>0$ a.s.,
      and $\max_{i,t} \mathbb{E}_{\phi}[M(Z_{it})^{8+\nu}]$
     is a.s. uniformly bounded over  $N,T$.
     In addition, we assume that $X_{it}$ is bounded uniformly  over $i,t,N,T$.

        \item[(v)] Concavity:

        For all $N,T,$

    $z \mapsto  \ell_{it} (z)$ is strictly concave over $z \in \mathbbm{R}$ a.s.
    Furthermore, there exist positive constants $b_{\min}$
    and $b_{\max}$ such that for all $z \in {\cal B}^0_{\varepsilon}$,
    $b_{\min} \leq -  \partial_{z^2} \ell_{it}(z)    \leq b_{\max}$ a.s.  uniformly over $i,t,N,T$.

       \item[(vi)] Strong factors: $\frac 1 N \sum_i (\alpha^0_i)^2 \to_P \sigma^2_\alpha >0$
   and
   $\frac 1 T \sum_t (\gamma^0_t)^2 \to_P \sigma^2_\gamma >0$.

     \item[(vii)] Generalized noncolinearity: For any $d_v$-vector $v$, define the coprojection matrix as ${\cal M}_{v} = I_{d_v} - v(v'v)v'$, where $ I_{d_v}$ denotes the identity matrix of order $d_v$. The $\dim \beta \times \dim \beta$ matrix with elements
        $$ D_{k_1k_2}(\gamma) =
        (NT)^{-1}
        {\rm Tr}( {\cal M}_{\alpha^0} X_{k_1} {\cal M}_{\gamma}  X_{k_2}'), \ \ k_1, k_2 \in \{1,...,\dim \beta \},$$
        satisfies
        $D(\gamma) > c >0 $ for all $\gamma \in \mathbbm{R}^T$, wpa1.

    \end{itemize}

\end{assumption}

We assume that the index $z_{it}^0$ is bounded. This condition holds if $X_{it}$, $\alpha_i$ and $\gamma_t$ are bounded. The relative rate of growth of $N$ and $T$ is chosen to produce a non-degenerate asymptotic distribution.  Assumption \ref{ass:PanelA1}$(i)-(v)$ are similar to Fernandez-Val and Weidner~\cite*{FW13}, so we do not discuss them further here.   The strong factor and generalized noncolinearity assumptions were previously imposed in Bai~\cite*{Bai:2009p3321} and Moon and Weidner~\cite*{MoonWeidner2013a,MoonWeidner2013b}  for linear models with interactive effects. Generalized noncolinearity rules out time and cross section invariant explanatory variables.

To describe the asymptotic distribution of the fixed effects estimator $\widehat \beta,$ it is convenient to introduce some additional
notation. Let $\overline{\cal H}$ be the $(N+T) \times (N+T)$ expected Hessian matrix of
the  log-likelihood with respect to the nuisance parameters evaluated at the true parameters, i.e.
\begin{align}
\overline{\cal H} = \mathbb{E}_{\phi}[ -  \partial_{\phi \phi'} {\cal L}] =
\left(\begin{array}{cc}  \overline{\mathcal{H}}_{(\alpha\alpha)} & \overline{\mathcal{H}}_{(\alpha\gamma)}  \\  {[\overline{\mathcal{H}}_{(\alpha\gamma)}]}'  & \overline{\mathcal{H}}_{(\gamma\gamma)}
\end{array}\right),
   \label{ExpectedHessian-MAIN}
\end{align}
where $\overline{\mathcal{H}}_{(\alpha\alpha)} =  \text{diag}(  \sum_{t} \mathbb{E}_{\phi}[- \partial_{z^2} \ell_{it}])/\sqrt{NT}$,
$\overline{\mathcal{H}}_{(\alpha\gamma)it} = \mathbb{E}_{\phi}[- \partial_{z^2} \ell_{it}]/\sqrt{NT}$,
and
$\overline{\mathcal{H}}_{(\gamma\gamma)}= \linebreak \text{diag}( \sum_{i} \mathbb{E}_{\phi}[- \partial_{z^2} \ell_{it}])/\sqrt{NT}$.
Furthermore, let
$\overline{\cal H}^{-1}_{(\alpha\alpha)}$, $\overline{\cal H}^{-1}_{(\alpha\gamma)}$,
$\overline{\cal H}^{-1}_{(\gamma\alpha)}$,
and $\overline{\cal H}^{-1}_{(\gamma\gamma)}$ denote the $N\times N$, $N\times T$, $T\times N$
and $T\times T$ blocks of the Moore-Penrose pseudoinverse $\overline{\cal H}^{-1}$ of $\overline{\cal H}$.
It is convenient to define the projection vector $\Xi_{it}$ and the residual $\tilde X_{it}$
 by
\begin{align}
   & \Xi_{it}
     := - \frac 1 {\sqrt{NT}} \sum_{j=1}^N \sum_{\tau=1}^T \left(
    \gamma^0_t \gamma^0_\tau \,  \overline{\cal H}^{-1}_{(\alpha\alpha)ij}
    + \alpha^0_i \gamma^0_\tau \,  \overline{\cal H}^{-1}_{(\gamma\alpha)tj}
    +  \gamma^0_t \alpha^0_j \, \overline{\cal H}^{-1}_{(\alpha\gamma)i\tau}
    +  \alpha^0_i \alpha^0_j  \, \overline{\cal H}^{-1}_{(\gamma\gamma)t\tau}
    \right)
     \; \mathbb{E}_\phi \left( \partial_{z^2}   \ell_{j\tau} X_{j\tau}
     \right) ,
   \nonumber \\
 & \tilde X_{it}:= X_{it} - \Xi_{it}.
   \label{DefProXi}
\end{align}
The $k$-th component of  $\Xi_{it}$ corresponds to the following population least squares projection
\begin{align*}
   \Xi_{it,k} &=  \alpha^{\ast}_{i,k}  \gamma^0_t + \alpha^0_i \gamma^{\ast}_{t,k} ,
   &
  \left(\alpha^{\ast}_{k} , \, \gamma^{\ast}_{k} \right)
   &= \operatorname*{argmin}_{\alpha_{i,k},\gamma_{t,k}} \sum_{i,t}
  \mathbb{E}_{\phi}( - \partial_{z^2} \ell_{it} )
        \left(  \frac{\mathbb{E}_{\phi}( \partial_{z^2} \ell_{it} X_{it})}
                        {\mathbb{E}_{\phi}( \partial_{z^2} \ell_{it} )}
         - \alpha^{\ast}_{i,k}  \gamma^0_t - \alpha^0_i \gamma^{\ast}_{t,k} \right)^2.
\end{align*}

Let $\overline{\mathbb{E}}  := \operatorname*{plim}_{N,T \to \infty}$.
The following theorem establishes the asymptotic distribution of the fixed effects estimator $\widehat \beta.$

\begin{theorem}[Asymptotic distribution of $\widehat \beta$]
  \label{th:BothEffects}
Suppose that Assumption \ref{ass:PanelA1} holds, that the following limits exist
\begin{align*}
   \overline B_{\infty} &=
      -  \overline{\mathbb{E}} \left[  \frac {1} {N}  \sum_{i=1}^{N}
            \frac{  \sum_{t=1}^T  \sum_{\tau=t}^T
            \gamma^0_t \gamma^0_\tau
        \mathbb{E}_{\phi}\left(
                \partial_{z} \ell_{it}  \partial_{z^2} \ell_{i\tau} \tilde X_{i\tau}
                 \right)
                 + \frac 1 2  \sum_{t=1}^T  (\gamma^0_t)^2
        \mathbb{E}_{\phi} ( \partial_{z^3} \ell_{it} \tilde X_{it} )   }
        {  \sum_{t=1}^T (\gamma^0_t)^2 \mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) }  \right]  ,
        \nonumber \\
      \overline D_{\infty} &=  -  \overline{\mathbb{E}} \left[
         \frac {1} {T}  \sum_{t=1}^{T}
            \frac{  \sum_{i=1}^N (\alpha^0_i)^2
        \mathbb{E}_{\phi}\left(
                \partial_{z} \ell_{it}  \partial_{z^2} \ell_{it} \tilde X_{it}
              +  \frac 1 2   \partial_{z^3} \ell_{it} \tilde X_{it}   \right)    }
        {  \sum_{i=1}^N  (\alpha^0_i)^2 \mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) } \right], \\
          \overline W_{\infty}  &=  - \overline{\mathbb{E}} \left[ \frac 1 {NT}  \sum_{i=1}^N
     \sum_{t=1}^T  \mathbb{E}_{\phi} \left(
              \partial_{z^2}  \ell_{it} \tilde X_{it} \tilde X'_{it} \right) \right],
   \end{align*}
and that $\overline W_{\infty}>0$.
Then,
   \begin{align*}
      \sqrt{NT} \left( \widehat \beta - \beta^0 \right)
          \; \to_d \;
       \overline{W}_{\infty}^{-1} {\cal N}( \kappa \overline B_{\infty}
                    + \kappa^{-1}  \overline D_{\infty} ,
           \;\overline W_{\infty}),
    \end{align*}
    so that  $\overline B_{\infty}^{\beta} =   \overline W_{\infty}^{-1} \overline B_{\infty}$ and $\overline D_{\infty}^{\beta} =   \overline W_{\infty}^{-1} \overline D_{\infty}$ in equation \eqref{eq: expansion}.
\end{theorem}

\medskip

It is instructive to evaluate the expressions of the bias also in our running examples.

\noindent  \textbf{Example \ref{example: linear}} (Linear model). \textit{ In the linear model with strictly exogenous explanatory variables, $Y_{it}  \mid X_{i}^T, \alpha, \gamma \sim \mathcal{N}(X_{it}'\beta + \alpha_i \gamma_t, \sigma^2)$ independently over $i$ and $t$, the expressions of the bias of Theorem~\ref{th:BothEffects} yield
$$
 \overline B_{\infty} =  \overline D_{\infty} = 0,
$$
which agree  with the no asymptotic bias result in Bai~\cite*{Bai:2009p3321} for homoskedastic linear models with interactive effects.
}

\noindent  \textbf{Example \ref{example: probit}} (Binary response model). \textit{In this case
$$\ell_{it}(z) = Y_{it} \log F(z) + (1 - Y_{it}) \log [1 -  F(z)],$$ so that $\partial_{z} \ell_{it} = H_{it} (Y_{it} - F_{it}),$   $ \partial_{z^2} \ell_{it} =   -  H_{it} \partial F_{it} + \partial H_{it} (Y_{it} - F_{it})$,  and $\partial_{z^3} \ell_{it} =  -  H_{it} \partial^2 F_{it} - 2 \partial H_{it} \partial F_{it} + \partial^2 H_{it} (Y_{it} - F_{it})$, where $H_{it} = \partial F_{it} / [F_{it}(1-F_{it})], and $   $\partial^{j}  G_{it} := \partial^{j} G(Z)|_{Z =z_{it}^0}$ for any function $G$ and $j = 0,1,2$. Substituting these values in the expressions of the bias of Theorem \ref{th:BothEffects} for the probit model with  all the components of $X_{it}$  strictly exogenous yields
\begin{eqnarray*}
\overline B_{\infty} &=&    \overline{\mathbb{E}} \left[
         \frac {1} {2N}  \sum_{i=1}^{N}
            \frac{  \sum_{t=1}^T (\gamma^0_t)^2 \mathbb{E}_{\phi}[\partial_{z^2} \ell_{it} \tilde{X}_{it} \tilde{X}_{it}']  } {  \sum_{t=1}^T (\gamma^0_t)^2 \mathbb{E}_{\phi}\left(\partial_{z^2} \ell_{it} \right) }\right] \beta^0 , \\ \overline D_{\infty} &=&    \overline{\mathbb{E}} \left[
         \frac {1} {2T}  \sum_{t=1}^{T}
            \frac{  \sum_{i=1}^N  (\alpha^0_i)^2 \mathbb{E}_{\phi}[\partial_{z^2} \ell_{it} \tilde{X}_{it} \tilde{X}_{it}'] } {  \sum_{i=1}^N (\alpha^0_i)^2 \mathbb{E}_{\phi}\left( \partial_{z^2} \ell_{it}\right) } \right] \beta^0.
\end{eqnarray*}
 The asymptotic bias  is therefore a positive definite matrix weighted average of the true parameter value as in the case of the probit model with additive  individual and time effects \cite{FW13}.}

\medskip

\noindent  \textbf{Example \ref{example: poisson} } (Count response model). \textit{In this case
$$\ell_{it}(z) = z Y_{it} - \exp(z) - \log Y_{it}!,$$
 so that $\partial_{z} \ell_{it} = Y_{it} - \omega_{it}$ and  $\partial_{z^2} \ell_{it} = \partial_{z^3} \ell_{it}= - \omega_{it} $, where $\omega_{it} = \exp(z_{it}^0)$. Substituting these values in the expressions of the bias of Theorem \ref{th:BothEffects} yields
\begin{eqnarray*}
\overline B_{\infty} &=&    - \overline{\mathbb{E}} \left[
         \frac {1} {N}  \sum_{i=1}^{N}
            \frac{  \sum_{t=1}^T  \sum_{\tau=t+1}^T
         \gamma^0_t \gamma^0_\tau \mathbb{E}_{\phi}\left[
               (Y_{it} - \omega_{it} ) \omega_{i\tau} \tilde X_{i\tau} \right]}
        {  \sum_{t=1}^T  (\gamma^0_t)^2 \mathbb{E}_{\phi}\left( \omega_{it} \right) } \right],
\end{eqnarray*}
and $\overline D_{\infty} = 0$.   If in addition
all the components of $X_{it}$ are strictly exogenous, then we get the no asymptotic bias result $\overline B_{\infty} = \overline D_{\infty} = 0$.}

\subsection{Asymptotic distribution of APEs}\label{subsec:apes}
In nonlinear models we are often interested in APEs, in addition to the model parameters. These effects
are averages of the data, parameters and unobserved effects; see expression
\eqref{eq: meffs}. For the panel models of Assumption \ref{ass:PanelA1} we specify the partial effects as $\Delta(Y_{it},X_{it}, \beta, \alpha_i, \gamma_t) = \Delta_{it}(\beta,  \alpha_i \gamma_t)$.
The restriction that the partial effects depend on $\alpha_i$ and $\gamma_t$ through $\pi_{it} =  \alpha_i \gamma_t$ is natural in our panel models since
$$
\mathbb{E} [Y_{it} \mid X^t_i, \alpha_i, \gamma_t, \beta] = \int y \exp [\ell_{it}(X_{it}'\beta + \pi_{it} )] dy,
$$
and the partial effects are usually defined as differences or derivatives of this conditional expectation with respect to the components of $X_{it}$. For example, the partial effects for the probit and Poisson
models and the scale parameter in the linear model described in Section \ref{sec:model} satisfy this restriction.

The distribution of the unobserved individual and time effects in general is not ancillary for the APEs, unlike for model parameters. We therefore need to make  assumptions on this  distribution  to define and interpret the APEs, and to derive the asymptotic distribution of their estimators. Here,  we control the heterogeneity of the partial effects assuming that the individual effects and explanatory variables are identically distributed cross sectionally and stationary over time so that the APE $\delta_{NT}^0$ does not change with $N$ and $T,$ i.e.  $\delta_{NT}^0 = \delta^0$.
We also impose  smoothness and moment conditions on the function $\Delta$ that defines the partial effects. We use these conditions to derive  higher-order stochastic expansions for the fixed effect estimator of the APEs and to bound the remainder terms in these expansions.  Let $\pi_{it}^0 = \alpha_i^0\gamma_t^0$, $\{\alpha_i\}_N := \{\alpha_i : 1 \leq i \leq N\}$, $\{\gamma_t\}_T := \{\gamma_t : 1 \leq t \leq T\},$ and $\{X_{it}, \alpha_i, \gamma_t \}_{NT} := \{(X_{it}, \alpha_i, \gamma_t)  : 1 \leq i \leq N, 1 \leq t \leq T\}.$

\begin{assumption} [Partial effects]   \label{ass:PanelA2} ~
  Let $\nu>0$, $\epsilon>0$, and let
     ${\cal B}^0_{\varepsilon}$ be a subset of $\mathbbm{R}^{\dim \beta+1}$
     that contains an $\varepsilon$-neighbourhood of $(\beta^0,\pi^0_{it})$
     for all $i,t,N,T$..

  \begin{itemize}
  \item[(i)] Sampling: for all $N,T,$   $\{X_{it}, \alpha_i, \gamma_t \}_{NT}$ is identically distributed across $i$ and/or stationary across $t$.

  \item[(ii)] Model: for all $i,t,N,T,$
  the partial effects depend on $\alpha_i$ and $\gamma_t$ through  $\alpha_i  \gamma_t$:
\begin{equation*}
\Delta(Y_{it},X_{it}, \beta, \alpha_i, \gamma_t) = \Delta_{it}(\beta, \alpha_i  \gamma_t).
\end{equation*}
The realizations of the partial effects are denoted by $ \Delta_{it} := \Delta_{it}(\beta^0, \alpha_i^0  \gamma_t^0).$

  \item[(iii)] Smoothness and moments: The function
       $(\beta,\pi) \mapsto \Delta_{it}(\beta,\pi)$
        is
      four times continuously differentiable over ${\cal B}^0_{\varepsilon}$ a.s.
      The partial derivatives of  $\Delta_{it}(\beta,\pi)$
      with  respect to the elements of $(\beta,\pi)$
      up to fourth order
      are bounded in absolute value uniformly over $(\beta,\pi) \in {\cal B}^0_{\varepsilon}$
      by a function $M(Z_{it})>0$ a.s.,
      and $\max_{i,t} \mathbb{E}_{\phi}[M(Z_{it})^{8+\nu}]$
     is a.s. uniformly bounded over  $N,T$.

    \item[(iv)] Non-degeneracy and moments:  $0 <  \min_{i,t} [\mathbb{E} (\Delta_{it}^2) - \mathbb{E}(\Delta_{it})^2] \leq \max_{i,t} [\mathbb{E} (\Delta_{it}^2) - \mathbb{E}(\Delta_{it})^2]  < \infty,$ uniformly over $N,T.$
 \end{itemize}
\end{assumption}

Analogous to $\Xi_{it}$ in equation \eqref{DefProXi}  we define
\begin{align}
   \Psi_{it}
    &= - \frac 1 {\sqrt{NT}} \sum_{j=1}^N \sum_{\tau=1}^T \left(
    \gamma^0_t \gamma^0_\tau \,  \overline{\cal H}^{-1}_{(\alpha\alpha)ij}
    + \alpha^0_i \gamma^0_\tau \,  \overline{\cal H}^{-1}_{(\gamma\alpha)tj}
    +  \gamma^0_t \alpha^0_j \, \overline{\cal H}^{-1}_{(\alpha\gamma)i\tau}
    +  \alpha^0_i \alpha^0_j  \, \overline{\cal H}^{-1}_{(\gamma\gamma)t\tau}
    \right)   \partial_{\pi} \Delta_{j\tau},
\end{align}
which also corresponds to a weighted least squares population projection.
We denote  the derivatives  of the partial effects $\Delta_{it}(\beta,\pi)$ by $\partial_\beta \Delta_{it}(\beta, \pi) := \partial  \Delta_{it}(\beta,\pi)/\partial \beta$,
$\partial_{\beta \beta'} \Delta_{it}(\beta, \pi) := \partial^2  \Delta_{it}(\beta,\pi)/(\partial \beta \partial \beta')$,
$\partial_{\pi^q} \Delta_{it}(\beta, \pi) := \partial^q \Delta_{it}(\beta,\pi)/\partial \pi^q$, $q = 1,2,3$, \textit{etc}.
We drop the arguments $\beta$ and $\pi$ when the derivatives are evaluated at the true
parameters $\beta^0$ and $\pi^0_{it} := \alpha_i^0  \gamma_t^0$, e.g.
$\partial_{\pi^q} \Delta_{it} := \partial_{\pi^q}\Delta_{it}(\beta^0,\pi^0_{it})$.

Let $\delta^0$ and $\widehat \delta$ be the APE and its fixed effects estimator, defined as in equations  \eqref{eq: meffs} and  \eqref{eq:ape}, where $\widehat \delta$ is constructed from a bias corrected estimators of the parameter $\beta$, i.e.
$\widehat \delta =  \Delta( \widetilde
\beta, \widehat \phi(\widetilde \beta)),
$
where $\widetilde \beta$ is such that $\sqrt{NT}(\widetilde \beta - \beta^0) \to_d N(0, \overline W_{\infty}^{-1})$.
The following theorem establishes the asymptotic distribution of $\widehat \delta.$
\begin{theorem}[Asymptotic distribution of $\widehat \delta$]
  \label{th:DeltaLimit}
   Suppose that the assumptions of Theorem~\ref{th:BothEffects}
   and Assumption~\ref{ass:PanelA2} hold, and that the following limits exist:
  \begin{align*}
    \overline B_{\infty}^{\delta} &=
     \overline{\mathbb{E}} \left[  \frac {1} {N}  \sum_{i=1}^{N}
            \frac{  \sum_{t=1}^T  \sum_{\tau=t}^T \gamma^0_t \gamma^0_\tau
        \mathbb{E}_{\phi}\left(
                \partial_{z} \ell_{it}     \partial_{z^2} \ell_{i\tau}  \Psi_{i\tau}
                 \right)  }
        {  \sum_{t=1}^T (\gamma^0_t)^2 \mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) } \right]
       \nonumber \\
          & \qquad
             -  \overline{\mathbb{E}} \left[  \frac {1} {2 \, N}  \sum_{i=1}^{N}
            \frac{  \sum_{t=1}^T (\gamma^0_t)^2
       \left[  \mathbb{E}_{\phi}(  \partial_{\pi^2} \Delta_{it} )
    -     \mathbb{E}_{\phi}( \partial_{z^3} \ell_{it} )
          \mathbb{E}_{\phi}( \Psi_{it} )       \right] }
        {  \sum_{t=1}^T (\gamma^0_t)^2 \mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) }   \right],
        \nonumber \\
      \overline D_{\infty}^{\delta} &=    \overline{\mathbb{E}} \left[
         \frac {1} {T}  \sum_{t=1}^{T}
            \frac{  \sum_{i=1}^N
            (\alpha^0_i)^2 \mathbb{E}_{\phi}\left(
                \partial_{z} \ell_{it}  \partial_{z^2} \ell_{it}    \Psi_{it}  \right)
     }
        {  \sum_{i=1}^N (\alpha^0_i)^2 \mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) } \right]
     \nonumber \\
       & \qquad
-  \overline{\mathbb{E}} \left[
         \frac {1} {2T}  \sum_{t=1}^{T}
            \frac{  \sum_{i=1}^N
         (\alpha^0_i)^2 \left[     \mathbb{E}_{\phi}(  \partial_{\pi^2} \Delta_{it} )
    -     \mathbb{E}_{\phi}( \partial_{z^3} \ell_{it} )
          \mathbb{E}_{\phi}( \Psi_{it} )       \right] }
        {  \sum_{i=1}^N (\alpha^0_i)^2 \mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) } \right],
   \nonumber \\
          \overline{V}_{\infty}^{\delta} &= \overline{\mathbb{E}} \left\{
       \frac {r_{NT}^2} {N^2T^2}
        \mathbb{E} \left[  \left(\sum_{i=1}^N \sum_{t = 1}^T  \widetilde \Delta_{it} \right)\left(\sum_{i=1}^N \sum_{t = 1}^T  \widetilde \Delta_{it} \right)' +  \sum_{i=1}^N \sum_{t=1}^T \Gamma_{it} \Gamma_{it}' \right] \right\},
  \end{align*}
for some deterministic sequence   $r_{NT} \to \infty$ such that $r_{NT} = \mathcal{O}(\sqrt{NT})$ and $ \overline{V}_{\infty}^{\delta} > 0,$
where $ \widetilde \Delta_{it} = \Delta_{it} - \delta^0$ and $\Gamma_{it} =   \overline{\mathbb{E}} \left[ (NT)^{-1} \sum_{i=1}^N \sum_{t=1}^T \partial_{\beta} \Delta_{it} \right]' \overline W_\infty^{-1} \partial_{z} \ell_{it}X_{it}
      -   \mathbb{E}_{\phi}( \Psi_{it} )
          \partial_{z} \ell_{it}$.
    Then,
    \begin{equation*}
    r_{NT} (\widehat \delta - \delta^0 -  T^{-1} \overline B_{\infty}^{\delta}
                    - N^{-1}  \overline D_{\infty}^{\delta}) \to_d \mathcal{N}(0 ,
           \;\overline V_{\infty}^{\delta}) .
    \end{equation*}
\end{theorem}

\begin{remark}[Convergence rate, bias and variance] \label{remark: conv_rate} The rate of convergence $r_{NT}$ is determined by the inverse of the first term of $\overline{V}_{\infty}^{\delta}$, which   corresponds to the asymptotic variance of $\delta := (NT)^{-1} \sum_{i=1}^N \sum_{t=1}^T \Delta_{it},$
$$
r_{NT}^{2} = \mathcal{O}\left(\frac{1}{N^2T^2} \sum_{i,j=1}^N  \sum_{t,s = 1}^T  \mathbb{E} [\widetilde \Delta_{it}   \widetilde \Delta_{js}'] \right)^{-1}.
$$
Assumption~\ref{ass:PanelA2}(iv) and the condition $r_{NT} \to \infty$ ensure that we can apply a central limit theorem to $\delta$. The exact rate of convergence in general depends on the sampling properties of the unobserved effects. For example, if  $\{\alpha_i\}_N$  and  $\{\gamma_t\}_T$ are independent sequences, and  $\alpha_i$ and $\gamma_t$ are independent for all $i,t$, then in general $r_{NT} = \sqrt{NT/(N+T-1)}$,
$$
          \overline{V}_{\infty}^{\delta} = \overline{\mathbb{E}} \left\{
       \frac {r_{NT}^2} {N^2 T^2}
       \sum_{i=1}^N \left[ \sum_{t, \tau = 1}^T \mathbb{E}( \widetilde \Delta_{it} \widetilde \Delta_{i \tau}' ) + \sum_{j \neq i}\sum_{t = 1}^T \mathbb{E}( \widetilde \Delta_{it} \widetilde \Delta_{j t} ') +  \sum_{t=1}^T \mathbb{E}(\Gamma_{it} \Gamma_{it}')\right] \right\},
$$
and the asymptotic bias is of order $T^{-1/2}+N^{-1/2}$.  The bias and the last term of $ \overline{V}_{\infty}^{\delta}$ are  asymptotically negligible in this case under the asymptotic sequences of Assumption~\ref{ass:PanelA1}(i).
\end{remark}

\noindent  \textbf{Example \ref{example: linear}} (Linear model). \textit{For $\delta = \sigma^2$, the convergence rate is $r_{NT} = \sqrt{NT}$ regardless of the sampling properties of the unobserved individual and time effects because $\Delta_{it} = (Y_{it} - X_{it}'\beta^0 - \pi^0_{it})^2$ is  independent over $i$ and $\alpha$-mixing over $t$.  The distribution of the unobserved  effects is ancillary for the APE because the information matrix of the log-likelihood $\ell_{it} = - .5 \log 2\pi - .5 \log \delta - .5 (Y_{it} - X_{it}'\beta - \pi_{it})^2/\delta$ is orthogonal in $\pi_{it}$ and $\delta$ at $\pi_{it} = \pi_{it}^0$ and $\delta = \delta^0$.
}

\subsection{Bias corrected estimators}
The results of the previous sections show that the asymptotic
distributions of the fixed effects estimators of the model parameters and APEs can have biases of the same
order as the  variances under sequences where $T$ grows at
the same rate as $N$. This is the large-$T$ version of the
incidental parameters problem that invalidates any inference based
on the asymptotic distribution. In this section we describe how to construct  analytical bias corrections for
panel models and give conditions for the asymptotic validity of
analytical and jackknife bias corrections.

The jackknife correction for the model parameter $\beta$  in equation \eqref{eq: jackknife2} is generic and applies to the panel model. For the APEs, the jackknife correction is formed similarly as
\begin{equation*}\label{eq: jack_apes}
\widetilde{\delta}_{NT}^{J} = 3  \widehat \delta_{NT} - \widetilde{\delta}_{N,T/2} - \widetilde{\delta}_{N/2,T},
\end{equation*}
where $\widetilde{\delta}_{N,T/2}$ is the average of the 2 split jackknife
estimators of the APE that leave out the first and second halves of the time
periods, and $\widetilde{\delta}_{N/2,T}$ is the average of the 2 split jackknife
estimators of the APE that leave out half of the individuals.

The analytical corrections are constructed using sample analogs of the expressions in Theorems \ref{th:BothEffects} and \ref{th:DeltaLimit}, replacing the true values of $\beta$ and $\phi$ by the  fixed effects estimators. To describe these corrections, we introduce some additional notation. For any function of the data, unobserved effects and parameters $g_{itj}(\beta,\alpha_i  \gamma_t,\alpha_i  \gamma_{t-j})$ with $0 \leq j < t$,  let $\widehat g_{itj} = g_{it}(\widehat \beta, \widehat \alpha_i  \widehat \gamma_t, \widehat \alpha_i  \widehat \gamma_{t-j})$ denote the fixed effects estimator,
e.g., $\widehat{\mathbb{E}_{\phi}[\partial_{z^2} \ell_{it}]}$ denotes the fixed effects estimator of $\mathbb{E}_{\phi}[\partial_{z^2} \ell_{it}].$
Let $\widehat{\cal H}^{-1}_{(\alpha\alpha)}$, $\widehat{\cal H}^{-1}_{(\alpha\gamma)}$,
$\widehat{\cal H}^{-1}_{(\gamma\alpha)}$,
and $\widehat{\cal H}^{-1}_{(\gamma\gamma)}$ denote the
blocks of the Moore-Penrose pseudo inverse matrix $\widehat{\cal H}^{-1}$, where
$$
\widehat{\cal H} =
 \left(\begin{array}{cc}  \widehat{\mathcal{H}}_{(\alpha\alpha)} & \widehat{\mathcal{H}}_{(\alpha\gamma)}  \\ {[\widehat{\mathcal{H}}_{(\alpha\gamma)}]}' & \widehat{\mathcal{H}}_{(\gamma\gamma)}
\end{array}\right) ,
$$
$\widehat{\mathcal{H}}_{(\alpha\alpha)} =  \text{diag}( -  \sum_{t} \widehat{\mathbb{E}_{\phi}[\partial_{z^2} \ell_{it}]})/\sqrt{NT}$, $\widehat{\mathcal{H}}_{(\alpha\alpha)} =  \text{diag}( -  \sum_{i} \widehat{\mathbb{E}_{\phi}[\partial_{z^2} \ell_{it}]})/\sqrt{NT}$, and $\widehat{\mathcal{H}}_{(\alpha\gamma)it} =
-  \widehat{\mathbb{E}_{\phi}[\partial_{z^2} \ell_{it}]}/\sqrt{NT}$.
Let
\begin{align*}
   & \widehat \Xi_{it}
     := - \frac 1 {\sqrt{NT}} \sum_{j=1}^N \sum_{\tau=1}^T \left(
    \widehat \gamma_t \widehat \gamma_\tau \, \widehat {\cal H}^{-1}_{(\alpha\alpha)ij}
    + \widehat \alpha_i \widehat \gamma_\tau \,  \widehat {\cal H}^{-1}_{(\gamma\alpha)tj}
    +  \widehat \gamma_t \widehat  \alpha_j \, \widehat {\cal H}^{-1}_{(\alpha\gamma)i\tau}
    +  \widehat \alpha_i \widehat  \alpha_j  \, \widehat {\cal H}^{-1}_{(\gamma\gamma)t\tau}
    \right)
     \; \widehat{\mathbb{E}_\phi \left( \partial_{z^2}   \ell_{j\tau} X_{j\tau}
     \right)} ,
   \nonumber \\
 & \widehat{\tilde X}_{it}:= X_{it} - \widehat \Xi_{it}.
\end{align*}
The $k$-th component of  $\widehat \Xi_{it}$ corresponds to the following least squares projection
\begin{align*}
   \widehat  \Xi_{it,k} &=  \widehat \alpha^{\ast}_{i,k}  \widehat  \gamma_t + \widehat  \alpha_i \widehat  \gamma^{\ast}_{t,k} ,
   &
  \left(\widehat \alpha^{\ast}_{k} , \, \widehat  \gamma^{\ast}_{k} \right)
   &= \operatorname*{argmin}_{\alpha_{i,k},\gamma_{t,k}} \sum_{i,t}
  \widehat {\mathbb{E}_{\phi}( - \partial_{z^2} \ell_{it} )}
        \left(  \frac{\widehat {\mathbb{E}_{\phi}( \partial_{z^2} \ell_{it} X_{it}})}
                        {\widehat{\mathbb{E}_{\phi}( \partial_{z^2} \ell_{it} )}}
         - \alpha^{\ast}_{i,k}  \widehat \gamma_t - \widehat  \alpha_i \gamma^{\ast}_{t,k} \right)^2.
\end{align*}

The analytical bias corrected estimator of $\beta^0$ is
$$
\widetilde \beta^A = \widehat \beta - \widehat W^{-1} \widehat B/T - \widehat W^{-1}  \widehat D/N,
$$
where
  \begin{align*}
   \widehat{B} &=
      -    \frac {1} {N}  \sum_{i=1}^{N}
            \frac{   \sum_{j=0}^L [T/(T-j)]  \sum_{t=j+1}^{T}  \widehat \gamma_t \widehat \gamma_{t-j}
        \widehat{\mathbb{E}_{\phi}\left(
                \partial_{z} \ell_{i,t-j}  \partial_{z^2} \ell_{it} \tilde X_{it}
                 \right)}
                 + \frac 1 2  \sum_{t=1}^T \widehat \gamma_t^2
        \widehat{\mathbb{E}_{\phi} ( \partial_{z^3} \ell_{it} \tilde X_{it} ) }   }
        {  \sum_{t=1}^T \widehat \gamma_t^2 \widehat{\mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) }}     ,
        \nonumber \\
      \widehat D &=  -
         \frac {1} {T}  \sum_{t=1}^{T}
            \frac{  \sum_{i=1}^N \widehat \alpha_i^2 \left[
        \widehat{\mathbb{E}_{\phi}\left(\partial_{z} \ell_{it}  \partial_{z^2} \ell_{it} \tilde X_{it}\right)}
              +  \frac 1 2  \widehat{\mathbb{E}_{\phi}\left(\partial_{z^3} \ell_{it} \tilde X_{it} \right) } \right]  }
        {  \sum_{i=1}^N \widehat \alpha_i^2 \widehat{ \mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) }}, \nonumber \\
        \widehat W  &=  -  (NT)^{-1}  \sum_{i=1}^N
     \sum_{t=1}^T    \widehat{\mathbb{E}_{\phi} \left(
              \partial_{z^2}  \ell_{it} \tilde X_{it} \tilde X'_{it} \right)}, \label{eq: se_parameter}
   \end{align*}
and $L$ is a trimming parameter for estimation of spectral expectations  such that $L \to \infty$ and $L/T \to 0$ \cite{HahnKuersteiner2011}.  The factor $T/(T-j)$ is a degrees of freedom adjustment that rescales the time series averages $T^{-1} \sum_{t=j+1}^T$ by the number of observations instead of by $T$. Unlike for variance estimation, we do not need to use a kernel function because the bias estimator does not need to be positive.
Asymptotic $(1-p)$--confidence intervals for the components of $\beta^0$ can be formed as
$$
\widetilde \beta_k^A \pm z_{1-p} \sqrt{\widehat W_{kk}^{-1} / (NT)},  \ \ k = \{1, ..., \dim \beta^0\},
$$
where $z_{1-p}$ is the $(1-p)$--quantile of the standard normal distribution, and $\widehat W_{kk}^{-1} $ is the $(k,k)$-element of the
matrix $\widehat W^{-1}$.

The analytical bias corrected estimator of $\delta^0$ is
$$
\widetilde \delta^A = \widehat \delta - \widehat B^\delta/T - \widehat D^\delta/N,
$$
where $\widehat \delta$ is the APE constructed from a bias corrected estimator of $\beta$. Let
\begin{align*}
  \widehat \Psi_{it}
    &= - \frac 1 {\sqrt{NT}} \sum_{j=1}^N \sum_{\tau=1}^T \left(
    \widehat \gamma_t \widehat  \gamma_\tau \,  \widehat {\cal H}^{-1}_{(\alpha\alpha)ij}
    + \widehat  \alpha_i \widehat  \gamma_\tau \,  \widehat {\cal H}^{-1}_{(\gamma\alpha)tj}
    +  \widehat  \gamma_t \widehat \alpha_j \, \widehat {\cal H}^{-1}_{(\alpha\gamma)i\tau}
    +  \widehat  \alpha_i \widehat  \alpha_j  \, \widehat {\cal H}^{-1}_{(\gamma\gamma)t\tau}
    \right)   \widehat{\partial_{\pi} \Delta_{j\tau}}.
\end{align*}
The fixed effects estimators of the components of the asymptotic bias  are
  \begin{align*}
    \widehat B^{\delta} &=  \frac {1} {N}  \sum_{i=1}^{N}
            \frac{  \sum_{j=0}^L [T/(T-j)] \sum_{t=j+1}^{T}
        \widehat \gamma_t \widehat \gamma_{t-j} \widehat{\mathbb{E}_{\phi}\left(
                \partial_{z} \ell_{i,t-j}     \partial_{z^2} \ell_{it}  \Psi_{it}
                 \right)}  }
        {  \sum_{t=1}^T \widehat \gamma_t^2  \widehat{\mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right)} }
                   \\ & \quad -   \frac {1} {2 \, N}  \sum_{i=1}^{N}
            \frac{  \sum_{t=1}^T \widehat \gamma_t^2
       \left[  \widehat{\mathbb{E}_{\phi}(  \partial_{\pi^2} \Delta_{it} )}
    -    \widehat{ \mathbb{E}_{\phi}( \partial_{z^3} \ell_{it} )}
          \widehat{\mathbb{E}_{\phi}( \Psi_{it} )   }    \right] }
        {  \sum_{t=1}^T \widehat \gamma_t^2 \widehat{\mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right)} }      ,
        \nonumber \\
    \widehat D^\delta  &=
          \frac {1} {T}  \sum_{t=1}^{T}
            \frac{  \sum_{i=1}^N \widehat \alpha_i^2
         \left[   \widehat{\mathbb{E}_{\phi}\left(
                \partial_{z} \ell_{it}  \partial_{z^2} \ell_{it}    \Psi_{it}  \right)}
     - \ft 1 2    \widehat{\mathbb{E}_{\phi}(  \partial_{\pi^2} \Delta_{it} )}
    + \ft 1 2    \widehat{\mathbb{E}_{\phi}( \partial_{z^3} \ell_{it} )}
          \widehat{\mathbb{E}_{\phi}( \Psi_{it} ) }      \right] }
        {  \sum_{i=1}^N  \widehat \alpha_i^2
 \widehat{\mathbb{E}_{\phi}\left(  \partial_{z^2} \ell_{i t} \right) }}.
  \end{align*}
The estimator of the asymptotic variance in general depends on the sampling properties  of the unobserved effects.   Under the independence assumption of Remark  \ref{remark: conv_rate},
 \begin{equation}\label{eq: se_ameff2}
         \widehat{V}^{\delta} =
       \frac {r_{NT}^2} {N^2 T^2}
       \sum_{i=1}^N  \left[  \sum_{t,\tau = 1}^T \widehat{\tilde \Delta}_{it} \widehat{\tilde \Delta}_{i\tau}' +  \sum_{t = 1}^T \sum_{j \neq i}  \widehat{\tilde \Delta}_{it} \widehat{\tilde \Delta}_{jt}' + \sum_{t=1}^{T} \widehat{\mathbb{E}_{\phi}( \Gamma_{it} \Gamma_{it}' )} \right],
       \end{equation}
  where  $ \widehat{\tilde \Delta}_{it} = \widetilde \Delta_{it} - \widehat \delta$.
Note that we do not need to specify the convergence rate to make inference because the standard errors $\sqrt{\widehat{V}^{\delta}}/r_{NT}$ do not depend on $r_{NT}$. Bias corrected estimators and confidence intervals can be constructed in the same fashion as for the model parameter.

We use the following homogeneity assumption to show the validity of the jackknife corrections for the model parameters and APEs.
It ensures that the asymptotic bias is the same in all the partitions of the panel. The analytical corrections
 {\it do not} require this assumption.
\begin{assumption}[Unconditional homogeneity] \label{assumption: stationarity} The sequence $\{(Y_{it}, X_{it}, \alpha_i, \gamma_t): 1 \leq i \leq N, 1 \leq t \leq T\}$ is  identically distributed across $i$ and strictly stationary
across $t,$ for each $N,T.$
\end{assumption}

\begin{remark}[Test of homogeneity] Assumption \ref{assumption: stationarity}  is a sufficient condition for the validity of the jackknife corrections. The weaker condition that the asymptotic biases are the same in all the partitions of the panel can be tested using the Chow-type test recently proposed in Dhaene and Jochmans  \cite*{DJ2014}.
\end{remark}

The following theorems are the main result of this section. They show that the analytical and jackknife  bias corrections eliminate the bias from the asymptotic
distribution of the fixed effects estimators of the model parameters and APEs without increasing variance, and that the estimators of the asymptotic variances  are consistent.

\begin{theorem} [Bias corrections for $\widehat \beta$] \label{th:bc} Under the conditions of Theorems \ref{th:BothEffects},
$$
\widehat W \to_P \overline{W}_{\infty},
$$
and, if $L \to \infty$ and $L/T \to 0,$
$$
\sqrt{NT}(\widetilde \beta^A - \beta^0)  \to_d \mathcal{N}(0,
\overline{W}_{\infty}^{-1}).
$$
Under the conditions of Theorems \ref{th:BothEffects} and Assumption \ref{assumption: stationarity},
$$
\sqrt{NT}(\widetilde \beta^J - \beta^0)  \to_d \mathcal{N}(0,
\overline{W}_{\infty}^{-1}).
$$
\end{theorem}

\begin{theorem} [Bias corrections for $\widehat \delta$] \label{th:bc_ameff} Under the conditions of Theorems \ref{th:BothEffects} and \ref{th:DeltaLimit},
$$
\widehat V^{\delta} \to_P \overline{V}^{\delta}_{\infty},
$$
and, if  $L \to \infty$ and $L/T \to 0,$
$$
r_{NT}(\widetilde \delta^A - \delta_{NT}^0)  \to_d \mathcal{N}(0,
\overline V_{\infty}^{\delta}).
$$
Under the conditions of Theorems \ref{th:BothEffects} and \ref{th:DeltaLimit},  and Assumption \ref{assumption: stationarity},
$$
r_{NT}(\widetilde \delta^{J} - \delta^0)  \to_d \mathcal{N}(0,
\overline V_{\infty}^{\delta}).
$$
\end{theorem}

\begin{remark}[Rate of convergence] The rate of convergence  $r_{NT}$ depends on the properties of the sampling process for the explanatory variables and unobserved effects (see remark \ref{remark: conv_rate}).

\end{remark}

\section{Numerical Examples} \label{sec:numeric}

To illustrate how the bias corrections work in finite samples, we consider the non-regression version of Example \ref{example: linear}, $Y_{it} \mid  \alpha, \gamma \sim \mathcal{N}(\alpha_i  \gamma_t, \sigma^2)$ independently over $i$ and $t$.
In this linear model the fixed effects estimator of $\phi_{NT}$ can be obtained  by the principal component method of Bai~\cite*{Bai:2009p3321}  or by Algorithm~\ref{algorithm:IFE-CMLE} with $\mathcal{L}_{NT}(\delta,\phi_{NT}) = - \sum_{i,t} (Y_{it} - \alpha_i \gamma_t)^2/2 $. Then, the fixed effects estimator of the APE $\delta= \sigma^2$ is
$$
\widehat \delta_{NT} = (NT)^{-1} \sum_{i,t} \left( Y_{it} - \widehat \alpha_i \widehat \gamma_t \right)^2.
$$

Applying the results of Theorem \ref{th:DeltaLimit} to $\Delta_{it} = (Y_{it} - \alpha_i \gamma_t)^2$, the probability limit of $\widehat \delta_{NT}$ admits the expansion
$$
\widehat{\delta}_{NT} =\delta^0 \left(1 - \frac{1}{ T} - \frac{1}{ N} \right) + o_P\left(\frac{1}{T} \vee \frac{1}{N} \right),
$$
as $N,T \to \infty$, so that $\overline{B}_{\infty}^{\delta} = -\delta^0$ and $\overline{D}_{\infty}^{\delta} = -\delta^0$.

To form the analytical bias correction we can set $\widehat{B}_{NT}^{\delta} = - \widehat \delta_{NT}$ and $\widehat{D}_{NT}^{\delta} = - \widehat \delta_{NT}$. This yields $\widetilde \delta^A_{NT} = \widehat \delta_{NT} (1 + 1/T + 1/N)$ with
$$
\widetilde{\delta}^A_{NT} = \delta^0 + o_P(T^{-1} \vee N^{-1}).
$$
This correction reduces the order of the bias, but it increases finite-sample variance because the factor $(1 + 1/T + 1/N) > 1$. We compare the biases and standard deviations of the fixed effects estimator and the corrected estimator in a numerical example below. For the Jackknife correction, straightforward calculations give
$$
\widetilde{\delta}^{J}_{NT} =  3 \widehat{\delta}_{NT} - \widehat{\delta}_{N,T/2} - \widehat{\delta}_{N/2,T}  = \delta^0 + o_P(T^{-1} \vee N^{-1}).$$

Table \ref{table:ns1} presents numerical results for the bias and standard deviations of the fixed effects and bias corrected estimators in finite samples obtained from 50,000 simulations. We consider panels with $N,T \in \{10,25, 50\},$ and only report the results for $T \leq N$ since all the expressions are symmetric in $N$ and $T$. All the numbers  in the table
are  in percentage of the true  parameter value, so we do not need to specify the value of $\delta^0$. We only report results based on the fixed effects estimator that uses Algorithm~\ref{algorithm:IFE-CMLE}, because the results based on the estimator that uses principal components are identical up to the tolerance level.\footnote{We set the tolerance criterium to $| \widehat \delta^{(m)} - \widehat \delta^{(m-1)} | < \epsilon_{tol} = 10^{-4}$.}  By comparing the first two rows of the table, we find that the first order approximation captures most of the bias of the fixed effects estimator.   The analytical and jackknife corrections offer substantial improvements in terms of bias reduction. The second and sixth row of the table show that the bias of the fixed effects estimator is of the same order of magnitude as the standard deviation, where $\overline{V}_{NT} = {\rm Var}[\widehat \delta_{NT}] = 2 (N-1)(T-1) (\delta^0)^2 / (NT)^2$  under independence of $Y_{it}$ over $i$ and $t$ conditional on the unobserved effects. The seventh row shows the increase in standard deviation due to analytical bias correction is small compared to the bias reduction, where $\overline{V}_{NT}^A = {\rm Var}[\widetilde \delta_{NT}^A] = (1+1/N+1/T)^2 \overline{V}_{NT}$. The last row shows that the jackknife yields less precise estimates than the analytical correction in small panels.  The asymptotic variance $\overline{V}_{\infty} = 2 (\delta^0)^2/(NT)$ in the fifth row provides a good approximation to the finite sample variance of all the estimators.

\begin{table}[htdp]
\begin{center}\caption{\label{table:ns1} Biases and Standard Deviations for $Y_{it} \mid \alpha, \gamma, \delta \sim \mathcal{N}(\alpha_i  \gamma_t, \delta)$}
\begin{tabular}{ccccccc} \hline\hline
&   N = 10 &  \multicolumn{2}{c}{N=25} & \multicolumn{3}{c}{N=50}  \\
   &   T = 10 & T=10  & T=25  & T=10  & T=25  & T=50  \\\hline
  $ (\overline{B}_{\infty}/T + \overline{D}_{\infty}/N) /\delta^0$   &  -.20 & -.14  & -.08  & -.12  & -.06  & -.04  \\
  $ (\widehat{\delta}_{NT} - \delta^0) /\delta^0$                          &  -.20 & -.14  & -.08  & -.12  & -.06  & -.04  \\
  $ (\widetilde{\delta}^A_{NT} - \delta^0)/\delta^0$                       & -.04 & -.02  & -.01  & -.01  &  .00  & .00  \\
  $ (\widetilde{\delta}^{J}_{NT}- \delta^0)/\delta^0$                      & .01   & .00  & -.01  & .00  & .00  & .00  \\\hline
  $ \sqrt{\overline{V}_{\infty}}/\delta^0$   &  .14 & .09  & .06  & .06  & .04  & .03  \\
  $ \sqrt{\overline{V}_{NT}}/\delta^0$      &  .13 & .08  & .05  & .06  & .04  & .03  \\
  $ \sqrt{\overline{V}^A_{NT}}/\delta^0$   &  .15 & .09  & .06  & .07  & .04  & .03  \\
  $ \sqrt{\overline{V}^J_{NT}}/\delta^0$   &  .18 & .10  & .06  & .07  & .04  & .03 \\\hline\hline
  \multicolumn{7}{l}{ \begin{footnotesize} Notes: Results obtained by 50,000 simulations \end{footnotesize}}
  \end{tabular}
\end{center}
\end{table}

Table \ref{table:ns2} illustrates the effect of the bias on the inference based on the asymptotic distribution. It shows the
coverage probabilities of 95\% asymptotic confidence intervals for $\delta^0$ constructed in the usual way as $$\text{CI}_{.95}(\widehat \delta) = \widehat \delta \pm 1.96  \widehat V_{NT}^{1/2} =
\widehat \delta (1 \pm 1.96  \sqrt{2/(NT)})$$
where $\widehat \delta = \{\widehat \delta_{NT}, \widetilde \delta_{NT}^{A},  \widetilde \delta_{NT}^{J}\}$ and $\widehat V_{NT} = 2 \widehat \delta^2/(NT)$ is an estimator of the asymptotic variance $\overline{V}_{\infty}$.  Here we find that the confidence intervals based on the fixed effect estimator display severe undercoverage  for all the sample sizes. The confidence intervals based on the corrected estimators have high coverage probabilities, which approach the nominal level as the sample size grows, as expected from the asymptotic results.

\begin{table}[htdp]
\begin{center} \caption{\label{table:ns2} Coverage probabilities for $Y_{it} \mid \alpha, \gamma, \delta \sim \mathcal{N}(\alpha_i  \gamma_t, \delta)$}
\bigskip

\begin{tabular}{ccccccc} \hline\hline
&   N = 10 &  \multicolumn{2}{c}{N=25} & \multicolumn{3}{c}{N=50}  \\
   &   T = 10 & T=10  & T=25  & T=10  & T=25  & T=50  \\\hline
  $\text{CI}_{.95}(\widehat \delta_{NT})$         &  .52  & .53  & .63  & .43  & .62  & .67  \\
  $\text{CI}_{.95}(\widetilde \delta^A_{NT})$   &  .88  & .91  & .93  & .92  & .94  & .94   \\
 $\text{CI}_{.95}(\widetilde \delta^J_{NT})$    &  .89  & .90  & .92  & .92  & .93  & .94   \\\hline\hline
   \multicolumn{7}{l}{\begin{footnotesize} Results obtained by 50,000 simulations. Nominal coverage probability is .95. \end{footnotesize}}
  \end{tabular}
\end{center}
\end{table}

\bibliographystyle{apa}

redpajama_set_name: RedPajamaArXiv


text:
Class of 2021 Arrives for Orientation Week
By Jingwen Zhang '18
Amherst College welcomed 473 new students from around the country and the world on Tuesday, Aug. 29, kicking off the college's orientation week, which included familiar programs from years past as well as new changes and improvements.
According to the Office of Admission, members of the class of 2021 were selected from a record-setting pool of 9,285 students, up 10 percent from last year. Of those applicants, 1,198, or 12.9 percent, were offered admission. One hundred and seventy-two students were admitted through early decision.
Students traveled to their new homes on the First-Year Quad from 388 secondary schools in 38 U.S. states and Puerto Rico as well as 26 countries. Of these students, 43 percent identify as domestic students of color. Men and women comprise nearly half the class each, with one student identifying as non-binary transgender.
The incoming class boasts record-high scores and academic achievements, with an average SAT composite score of 2232 and ACT composite of 33. This year's class was also the first to take the SAT in its new format. Eighty-two percent of students ranked in the top decile of their high schools' graduating classes.
Fifty-five percent of new students are receiving financial aid, and 11 percent are first-generation college students. In addition, 16 are transfer students, including two U.S. veterans.
Dean of Admission and Financial Aid Katie Fretwell '81 said in an email interview that the new class brings "a tremendous array of talents and interests across the academic disciplines."
"As a group, they have the distinction of having particularly strong aspirations for careers in diplomacy and foreign service and have had an unusually high participation rate in Model United Nations programs through their secondary schools," Fretwell added.
This year's orientation week includes familiar elements such as squad meetings, Sexual Health Educator (SHE) skits, the DeMott Lecture and the "Voices of the Class" performance. Meetings on subjects like sexual respect and addressing bias will build on themes from previous years, but Dean of New Students Rick López said in an email interview that the format of some orientation events continues to "[move] away from having students listen to speeches" and toward "redesigning orientation events into small group dialogues."
López said that some other changes geared toward students include longer academic advising and registration periods, a reception geared toward first-generation and low-income students, and at the request of student government members, the return of the class-wide Honor Code signing event.
Also new to orientation are residence-hall specific dinners. "[Their] purpose is to help students create their own dorm identity, while also bonding with students in nearby dormitories," López said. "Like all other events in orientation, our focus is on fomenting dialogue while creating community."
Many students' families accompanied them to campus to participate in orientation programming on Tuesday that was designed with guests in mind. President Biddy Martin addressed students and families in an all-new "President's Welcome" event.
Receptions for guests and families in Spanish, Mandarin and Korean were also held on the first day. The Korean and Mandarin-language receptions were new this year.
López initiated the first such event for Spanish-speaking family members three years ago. "The session proved to be such a hit … This year we looked at our student body to think about whether we can extend the program to other languages," he said. "We found that the two other languages that are most commonly spoken in students' homes are Korean and Mandarin."
According to López, these language-specific receptions featuring faculty, students and staff were designed following students' feedback that some parents and family members could feel more welcome and better support their students after attending an informational session in the language most comfortable to them.
At the end of the first day of orientation, students were able to spend time with their families prior to their departure in a two-hour "Family Block" time that was incorporated into the schedule.
On Friday, students departed from campus for Learn, Explore, Activate and Participate (LEAP) programs, which focus on a specific topic or field of exploration with the added goal of bringing students closer together in small groups. In addition to longtime programs such as First-Year Outdoor Orientation Trips (FOOT) and Community Engagement Orientation Trips (CEOT), this year had a new addition — "Discover The Distant Past by Land, Sea and Air" — designed to introduce students to the region's natural history.
On Sunday, students will return from LEAP. Convocation and the annual student organizations' involvement fair will take place on Labor Day, and Tuesday will mark the first day of classes.


text:
/*
 * This file is generated by jOOQ.
 */
package stroom.processor.impl.db.jooq.tables;

import stroom.processor.impl.db.jooq.Keys;
import stroom.processor.impl.db.jooq.Stroom;
import stroom.processor.impl.db.jooq.tables.records.ProcessorNodeRecord;

import org.jooq.Field;
import org.jooq.ForeignKey;
import org.jooq.Identity;
import org.jooq.Name;
import org.jooq.Record;
import org.jooq.Row2;
import org.jooq.Schema;
import org.jooq.Table;
import org.jooq.TableField;
import org.jooq.TableOptions;
import org.jooq.UniqueKey;
import org.jooq.impl.DSL;
import org.jooq.impl.SQLDataType;
import org.jooq.impl.TableImpl;

import java.util.Arrays;
import java.util.List;

/**
 * This class is generated by jOOQ.
 */
@SuppressWarnings({ "all", "unchecked", "rawtypes" })
public class ProcessorNode extends TableImpl<ProcessorNodeRecord> {

    private static final long serialVersionUID = 1L;

    /**
     * The reference instance of stroom.processor_node
     */
    public static final ProcessorNode PROCESSOR_NODE = new ProcessorNode();

    /**
     * The class holding records for this type
     */
    @Override
    public Class<ProcessorNodeRecord> getRecordType() {
        return ProcessorNodeRecord.class;
    }

    /**
     * The column stroom.processor_node.id.
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    public final TableField<ProcessorNodeRecord, Integer> ID = createField(DSL.name("id"), SQLDataType.INTEGER.nullable(false).identity(true), this, "");

    /**
     * The column stroom.processor_node.name.
     */
    public final TableField<ProcessorNodeRecord, String> NAME = createField(DSL.name("name"), SQLDataType.VARCHAR(255).nullable(false), this, "");

    private ProcessorNode(Name alias, Table<ProcessorNodeRecord> aliased) {
        this(alias, aliased, null);
    }

    private ProcessorNode(Name alias, Table<ProcessorNodeRecord> aliased, Field<?>[] parameters) {
        super(alias, null, aliased, parameters, DSL.comment(""), TableOptions.table());
    }

    /**
     * Create an aliased stroom.processor_node table reference
     */
    public ProcessorNode(String alias) {
        this(DSL.name(alias), PROCESSOR_NODE);
    }

    /**
     * Create an aliased stroom.processor_node table reference
     */
    public ProcessorNode(Name alias) {
        this(alias, PROCESSOR_NODE);
    }

    /**
     * Create a stroom.processor_node table reference
     */
    public ProcessorNode() {
        this(DSL.name("processor_node"), null);
    }

    public <O extends Record> ProcessorNode(Table<O> child, ForeignKey<O, ProcessorNodeRecord> key) {
        super(child, key, PROCESSOR_NODE);
    }

    @Override
    public Schema getSchema() {
        return aliased() ? null : Stroom.STROOM;
    }

    @Override
    public Identity<ProcessorNodeRecord, Integer> getIdentity() {
        return (Identity<ProcessorNodeRecord, Integer>) super.getIdentity();
    }

    @Override
    public UniqueKey<ProcessorNodeRecord> getPrimaryKey() {
        return Keys.KEY_PROCESSOR_NODE_PRIMARY;
    }

    @Override
    public List<UniqueKey<ProcessorNodeRecord>> getUniqueKeys() {
        return Arrays.asList(Keys.KEY_PROCESSOR_NODE_PROCESSOR_NODE_NAME);
    }

    @Override
    public ProcessorNode as(String alias) {
        return new ProcessorNode(DSL.name(alias), this);
    }

    @Override
    public ProcessorNode as(Name alias) {
        return new ProcessorNode(alias, this);
    }

    /**
     * Rename this table
     */
    @Override
    public ProcessorNode rename(String name) {
        return new ProcessorNode(DSL.name(name), null);
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    /**
     * Rename this table
     */
    @Override
    public ProcessorNode rename(Name name) {
        return new ProcessorNode(name, null);
    }

    // -------------------------------------------------------------------------
    // Row2 type methods
    // -------------------------------------------------------------------------

    @Override
    public Row2<Integer, String> fieldsRow() {
        return (Row2) super.fieldsRow();
    }
}

redpajama_set_name: RedPajamaGithub


Modern Brits are letting their creativity die, according to a recent study. We're more used to taking than making – and it's a crisis that's infecting the Church as well.
Most Brits (63 per cent) are neglecting their creative talents, and one in five adults over 30 have abandoned their artistic interests, according to a study by BIC®, published last week.
PixabayIs the Church - like most Brits - rejecting creativity in an increasingly busy world?
The cause of decline? Many (85 per cent) pointed to constant internet connectivity, with an abundance of devices and the prevalence of social media making it far easier to plug in or switch on than it is to pick up a pen and paper.
The busyness of modern life was also a factor (26 per cent) alongside 'family commitments' (20 per cent). But over a third had abandoned creative talents such as musical instruments, writing or drama because they just 'weren't good at it any more'.
Consumerism now comes easier than creativity – but the same is true in the Church, and it's a serious problem.
In my University years, I led a society that was all about encouraging Christians to use their creative gifts. You could gather hundreds for a society that united around evangelism, but could you gather even half as many who wanted to use their creativity to worship God?
Sadly, not quite. My experience tells me that many Christians have significant creative talents, but a minority of them would see investing in them as a major priority. Others might not have an obvious creative streak, but quite possibly that's because no one ever encouraged them to try to find it.
Of course, the Church might elevate a few 'creators' – those in the worship band for example – but the average Sunday sees the rest of the congregation relegated to the role of Christian consumer. How did we get here?
The advances of modern technology have served humanity in a myriad ways. They've dramatically expanded our horizons – but also narrowed them by often rendering us as passive receivers, not active creators. The internet offers a sea of compelling content to enjoy, but all that entertainment can inhibit our capacity to imagine and make.
Our connectivity can also engender constant comparison. Some might be inspired by social media to make and share their own innovations, but others might be so intimidated by the talent they see online that they neglect to create. They fear doing it badly, so don't do it at all.
Fear of 'bad art' isn't wrong, especially in the Christian world, where it's fair to say not all artistic efforts (certain 'faith-basedmovies' spring to mind) have been stellar. However, any artist knows that their industry will include flaws and miss-fires, but they press on, it's how they get to the gold. So why is Christian artistry important?
A neglect of artistry in the Church would have shocked the authors of Scripture, whose own work often constituted deeply artistic storytelling. And creativity drips off the very first pages of the Bible – in Genesis we meet the God who creates, bringing light from darkness, order from chaos and a universe where there wasn't one before.
Much has been made of God's making humankind 'in his own image' (Genesis 1:27) but that notion, whatever else it means, must surely include the image of the God who – up to that point – has done nothing but create.
And humanity has often followed that image – consider the immense creativity needed to take us from a race that hadn't learned to fish to one that now largely rules the skies and seas with our towering technological innovations. God invited humanity to take the garden and build a city – and that means creating and cultivating.
It's ironic that 'arts' subjects are now so often maligned as largely useless pursuits. Modern education tends to favour hard sciences and fields like mathematics and economics for their apparent bankability. But without artistry, we would have so little that we enjoy.
Fellowship for Performing ArtsMax McLean as CS Lewis' dramatic demon 'Screwtape' in a stage version of Lewis' 'The Screwtape Letters'.
If a song ever made you cry, if a joke ever made you laugh, if a movie ever moved you or words ever made you wonder at the world – then you know the value of art. No one wants a world without these things, but are we that interested in keeping them around?
Writers like CS Lewis have shown how artistry can be a form of apologetics or evangelism. In The Chronicles of Narnia Lewis invited his audience to imagine a magical, enchanted world – and then wonder if his Good v Evil 'fairy-tale' might actually be a true story about reality.
We can forget that creativity is not only a gift to others but a gift to ourselves. It doesn't have to be useful or successful to have value. The mere process of writing a song, drawing a picture or telling a story can be a form of therapy. Just like our physical body, our imaginations need exercise so that we stay healthy.
In contrast, we often think just consuming entertainment will give us 'rest' – but its passivity can just make us unhappy.
The Christian can say why: creating feels right because it fulfils the 'image' in which we were made. Only taking and never making does the exact opposite.
Some will inevitably relegate artistry to the sidelines if they think they must choose between that and 'preaching the gospel'. But they aren't mutually exclusive. I think of three people I've met in the past year: the pastor writing songs as an outlet for praise and pain as he battles with cancer, the Christian director using secular theatre as a way of engaging a modern conversation about God, or the comedian who uses stand-up as an alternative evangelism. They're reshaping the world around them and telling a story with it.
Creativity offers people an profound, essential way of connecting with God, each other and themselves. The Church should cherish it, and – before everyone forgets – show the rest of the world what a gift it can be.


text:
Die City Preachers gelten als erste Folk-Rock-Gruppe Deutschlands.

Geschichte
Gegründet wurde die Band 1965 in Hamburg von dem aus London stammenden Bankangestellten John O'Brien-Docker. Die Musik war eine Mischung von Folklore, später Folk genannt, aus aller Welt: Flamenco aus Spanien, Blues aus den USA, Irish Folk, Bouzouki-Klänge aus Griechenland, jiddische und Balkan-Lieder, aber auch frühe deutschsprachige Protestsongs sowie niederdeutsche Lieder.

Die City Preachers traten bis in die 1970er Jahre hinein in wechselnden Besetzungen auf. Die Zahl der Bandmitglieder schwankte zwischen fünf und zehn. Die Schallplatten der Band verkauften sich recht gut.

Aus der Band gingen namhafte Musiker hervor. Dazu gehören neben dem Gypsy-Swing-Gitarristen John O'Brien-Docker und dem Sänger und Fernsehschaffenden Kalle Freynik die Sängerinnen Inga Rumpf, Sibylle Kynast, Dagmar Krause, der Sänger, Kunstpfeifer und Multiinstrumentalist Eckart Kahlhofer, der Keyboarder Jean-Jacques Kravetz und der Schlagzeuger und spätere Sänger Udo Lindenberg. Insgesamt wirkten über 20 Solisten in dieser Band in wechselnden Besetzungen nach dem sogenannten "Baukastenprinzip" mit, das heißt "Jeder ist Solist" und "Jeder spielt mit Jedem". So unterschiedliche Sängerinnen wie Inga Rumpf, Sibylle Kynast und Dagmar Krause sangen über mehrere Jahre hinweg neben- und miteinander in der Gruppe.

Inga Rumpf, Dagmar Krause, Karl-Heinz Schott, Udo Lindenberg und Jean-Jacques Kravetz entfernten sich 1969 immer mehr von der Folk-Musik. Udo Lindenberg schied aus und spielte Schlagzeug bei Peter Herbolzheimer und Klaus Doldinger, bevor er 1973 eine Solokarriere begann. Dagmar Krause ging nach England (Slapp Happy). Inga Rumpf, Karl-Heinz Schott, der neue Schlagzeuger Carsten Bohn und Jean-Jacques Kravetz wählten den Bandnamen Frumpy.

1970 trafen sich Dagmar Krause, Sibylle Kynast, Elga, Jürgen Stielow, Eckart Kahlhofer und Michael Laukeninks zu einer City-Preachers-Produktion im Studio, um die LP Back to the City aufzunehmen, die 1971 auf dem Hörzu/Metronome-Label veröffentlicht wurde.

Michael Laukeninks, Manager und Produzent der City Preachers, arbeitete als Lektor bei den Schacht-Musikverlagen, 1971 als Promoter bei WEA Records und 1973 als Redakteur beim NDR. Bis zu seinem Tod am 22. Juli 2018 war er darüber hinaus als Fotograf tätig.

Diskografie
Alben
 1965: Folklore (Teldec)
 1966: Die City Preachers (Decca)
 1966: Warum? (Philips)
 1967: Cool Water – Internationale Folk Hits (Decca)
 1968: Der Kürbis, die Traumtänzer und das Transportproblem (Decca)
 1971: Back to the City (Hörzu/Metronome)
 1982: Inga Rumpf and the City Preachers (Teldec)
 1998: Folklore (CD, Teldec)
 1998: Inga Rumpf: In the Beginning (CD, Teldec)
In den 60er und 70er Jahren erschienen weitere LPs, teils als Soloprojekte oder als spezielle Zusammenstellungen für Bücherclubs und für Labels im Ausland. Auch einige Singles sind veröffentlicht worden.

Weblinks

 City Preachers jüngste gute Archivversion von citypreachers.de auf web.archive.org; Hauptseite
 City Preachers jüngste gute Archivversion von citypreachers.de/content1.html auf web.archive.org; Mitglieder der City Preachers

Einzelnachweise

Folkband
Deutsche Band
Band (Hamburg)

redpajama_set_name: RedPajamaWikipedia