# Tagged Questions

The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

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489 views

### Variance on the sum of predicted values from a mixed effect model on a timeseries

I have a mixed effect model (in fact a generalized additive mixed model) that gives me predictions for a timeseries. To counter the autocorrelation, I use a corCAR1 model, given the fact I have ...
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1k views

### How to estimate variance components with lmer for models with random effects and compare them with lme results

I performed an experiment where I raised different families coming from two different source populations, where each family was split up into a different treatments. After the experiment I measured ...
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133 views

### Variance of the Kaplan-Meier estimate for dependent observations

Can someone help me find a way to estimate the variance of the Kaplan-Meier estimate with dependent observations? Specifically, I have failure time data from patients with several different ...
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127 views

### How to test equality of variances with circular data

I am interested in comparing the amount of variability within 8 different samples (each from a different population). I am aware that this can be done by several methods with ratio data: F-test ...
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224 views

### How does pooling and resampling affect variance of sample mean?

Suppose I have $N$ independent random variables $X_n$. I draw a sample of predetermined size $K_n$ from each of them. Denote the average of each sample $\bar{\hat{X}}_n$, and the total number of ...
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63 views

### k-subset with maximal variance

I have two versions of the same question: Given a list of numbers (with possible duplicates), how to find a k-subset (with possible duplicates) that maximize the variance? is there a more efficient ...
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168 views

### How does number of observations supporting alternate hypothesis on a test of a variance have to scale so that null is rejected?

Informal explanation: In the course of my research I've run into the following problem: I am observing a machine that outputs random numbers. Most (if not all) of these random numbers come from the ...
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50 views

### Bounds for the population variance?

Suppose we have i.i.d. samples $x_1$, $\ldots$, $x_n$ for a (potentially non-normal) random variable $X$ with finite moments. We can use these samples to construct an unbiased estimates of the ...
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501 views

### How do I interpret the covariance matrix from a curve fit?

I'm not too great at statistics, so apologies if this is a simplistic question. I am fitting a curve to some data, and sometimes my data best fits a negative exponential in the form \$a * e^{(-b * x)} ...
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184 views

### Link between variance and pairwise distances within a variable

Please, prove that if we have two variables (equal sample size) $X$ and $Y$ and the variance in $X$ is greater than in $Y$, then the sum of squared differences (i.e., squared euclidean distances) ...
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39 views

### Can the OLS residual variance suggest a polynomial relationship?

I am trying to figure out whether from the following graph of the OLS residuals that the linear relationship does not hold, and that probably a cubic relationship would do better? Since both in the ...
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32 views

### Bound on the variance for [0,1] RVs as a function of the mean

I noticed that if $X$ is a RV in $[0,1]$ then $V[X] \leq E[X](1-E[X])$, which also implies that the bernoulli distribution maximizes variance (one of many solutions). For interest's sake consider ...
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54 views

### Finding correlation coefficient

if I have A and B with the following known variables: with $E[A]$, $E[B]$ , $\sigma_{A}$ , $\sigma_B$ and correlation coefficient: $\rho_{AB}$ (assign numbers if you like) Say: $C=0.6A+0.4B$ Then ...
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50 views

### Combined variance following multiple imputation with survival model

I have created 5 imputations of a dataset and have fit a survival model to them all in R. I want to combine the estimates of the coefficients and the standard errors of the coefficients. To do this I ...
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57 views

### How to assess stability of daily time series in sentiment analysis?

I developed a measure of "sentiment" and I have time based data and used the measure to derive a daily sentiment time series. I am looking for some way to establish reliability or maybe stability. For ...
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41 views

### An investment and variance question for monthly payments

I have a question regarding a financial/statistical problem. How do you calculate the variance of the outcome of an investment in a stock, when the investment is so called time diversified, i.e. ...
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72 views

### Can we approximate the distribution of S?

I want to understand how the sampling distribution of the whole covariance matrix behaves for large $n$. I am trying to use the delta method and multivariate CLT. I am trying to show that when the ...
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106 views

### Do we need an unbiased estimator of the variance?

"Although it is nice to have an unbiased estimator of the variance, we do not really need it to understand the relation between our independent variable and our dependent variable. Why?" I think I ...
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126 views

### How to fix the constant variance assumption?

We have a project where we have to find the best model using a large set of data. In our current model there are 10 variables, some quantitative, and a few that are qualitative. When we first do ...
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114 views

### What prior distributions could/should be used for the variance in a hierarchical bayesisan model when the mean variance is of interest?

In his widely cited paper Prior distributions for variance parameters in hierarchical models (916 citation so far on Google Scholar) Gelman proposes that good non-informative prior distributions for ...
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177 views

### What is point-wise variance?

While reading The Elements of Statistical Learning, I've encountered the term "point-wise variance" several times. While I have a vague idea of what it likely means, I'd be grateful to know How is ...
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109 views

### Correct variance for minimum detectable difference

I have a question regarding variance, paired testing and minimum detectable difference (MDD). Paired samples: $$MDD (δ) = \sqrt{ \frac{σ^2}{n} (t_{(α/2,n-1)} + t_{(1-β, n-1)})}$$ I have a set of ...
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255 views

### R limma voom function mean-variance trend

I am using the limma package in R to do some analysis on a count data matrix. I use the voom function and that normally creates a plot with the mean variance trend line in it. Now I created also a ...
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163 views

### Univariate- Variance preserving, order reversing transformation

This is a soft question: How can the order of a sample univariate data be reversed while preserving the variance?
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89 views

### Generalized Linear Models and Curse of Dimensionality

I was wondering what happens to bias and variance of GLM estimates as dimensionality approaches the number of training data points? Specifically in Linear Regression and Poisson Regression? I know ...
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174 views

### Does pooled variance correct for/protect from unequal variance when calculating effect size?

This may be a lame question, but I got stuck and can't get my head around it. I am running a gene expression analysis, comparing ~10000 genes between two groups, n=6 samples per group. My pipeline ...
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161 views

### Bootstrap variance of squared sample mean

The following is question 8 of chapter 8 in Wasserman's All of Statistics: Let $T_n = \overline{X}_n^2$, $\mu = \mathbb{E}(X_1)$, $\alpha_k = \int|x - \mu|^kdF(x)$, and \$\hat{\alpha}_k = ...
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134 views

### Cramer-Rao type bound for Information Gain

I am interested in the Bayes risk of some distribution $\pi$ $$r(\pi) = \mathbb{E}_{\pi(x)}[ \mathbb{E}_{\Pr(y|d,x)}[L(x,\hat x(y|d))]],$$ where $L$ is some loss function and $\hat x$ is the ...
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44 views

### Looking for formalization of the idea of low-variance predictors

In baseball, Bill James suggested using, to predict next season's winning percentage runs_scored^2/(runs_scored^2 + runs_allowed^2), rather than this season's ...
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220 views

### How to create a ratio distribution from samples?

Ok, let's try again. The context of the original question is given below, but perhaps it helps to focus on the statistical aspect to get an answer. What I got is a number of measurements in unit t. ...
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383 views

### How can this series pass the structural change test?

I have this series: ...
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95 views

### How to show that the variances of 2 sets of 3D points are different?

I have 2 point clouds (3D points). I can visually tell that the spread in one cloud is much larger than the other, and I have also plotted their error ellipsoids. Now, I'm looking for a statistical ...
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9 views

### Are the sequential sum of squares appropriate when treatments must be applied in sequence?

I'm working with some modeled future stream flow data that was created in two steps. First, future precipitation predictions (at certain points in a watershed) were created by running historical ...
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22 views

### What coefficient could I use to calculate the relative difficulty of a test in relation to others using only mean and population standard deviation?

I have a series of tests, all of them of different difficulty, and from each of them I get an average score and a population standard deviation; e.g: ...
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36 views

### Interpretation of Variance and Covariance

I am totally new to statistics and I have to create a variance and covariance analysis. I am using SPSS for this. I have created the covariance table: Hopefully it is the right thing. The first 3 ...
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49 views

### Mean and variance of call center data

I have a fairly involved homework question, I was wondering if I could get some help. There are two types of phone calls arriving at a switch, long-duration and short-duration. Each day the number ...
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30 views

### Measuring relative variability for variables with different scales

I want to compare the relative variability of several sleep-related variables in the same group of subjects. For example, is there more variability in time spent in REM sleep compared to the number of ...
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35 views

### Variance associated with factors in GLS (nlme)

First time posting here, so thank you ahead of time for your help. I'd like to estimate the variances associated with two factors in a relatively simple, but unbalanced GLS model, and I am unsure how ...
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68 views

### Variance of powers of a random variable

Is it possible to derive a formula for variance of powers of a random variable in terms of expected value and variance of X? $$\operatorname{var}(X^n)= \,?$$ and $$E(X^n)=\,?$$
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129 views

### Finding the UMVUE of the variance of a gaussian with mean zero

Given $Z_1, ..., Z_n, \sim\mathcal{N}(0, θ^2), θ>0$. Define $X_i=|Z_i|$ and consider estimation of $\theta$ and $θ^2$ on the basis of the random sample $X_1,...X_n$. Find the uniformly minimum ...
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87 views

### error variance calculations for reliability analysis of a composite metric in HLM

I am trying to determine how to obtain within-group variance for a composite measure based on a set of (weighted) proportions. I have 50 groups being compared on 8 proportion measures, with 4 ...
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40 views

### Why do different estimators for stock volatility exist? (Realized Variance, RAV, etc)

I am very confused about why different volatility estimators (RV, RAV, BPV, etc) exist. If the goal is to find the best estimator for stock volatility, and volatility is latent, how do I know which ...
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69 views

### Compound poisson process: Average size of claim will exceed £110

"An insurance company receives claims at a rate of two per week, the size of a claim in pounds having mean 100 and standard deviation 50. Assuming the compound Poisson process as a model, and using ...
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87 views

### Confidence Interval in Monte Carlo integration

I want to integrate $\int_{\mathbb{R}_+}\mathbb{1}_A(x) d\mathbb{P}(x)$, in other words I am interested in $\mathbb{P}(A)$. I did this numerically with two Monte Carlo steps. First, I drew, say a ...
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43 views

### How to compute variance of a continuous time sequence?

I am observing two continuous time-series where at every instant in time I may observe a unary event. That is, for each sequence, say $S_1$, I have a data set comprised of $S_1 = (t_0, t_1, ..., t_m)$ ...
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56 views

### Different Mean Square partitions in an unbalanced bifactorial ANOVA (with random factor) between R and Statistica

I am trying to extract variance components for selection and chance in a bifactorial design with Generation as a fixed factor and Replicate as a random term, for early fecundity. Since I am using ...
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164 views

### When are the asymptotic variance of OLS and 2SLS equal?

Assume the model $\ y = X\beta + u \$ with $\ W \$ is a $\ n\times l \$ so called matrix of instruments. The following assumptions hold. There is a law of large numbers (LLN) for 1.,2.,3. and ...
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149 views

### Determining Optimal Number of Cluster in Hierarchical Clustering in Consideration of Variance of Data

I'm applying a Hierarchical Agglomerative Clustering (HAC) for grouping my data and I need to determine the number of the cluster automatically. To determine the optimal number of cluster, I obtain ...
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110 views

### Variance decomposition in linear regression model

Consider the linear model $y = \mathbf{X}\mathbf{\beta} + \epsilon$. The residual variance-covariance matrix is given by $\text{Var}(\epsilon)$. Greene's textbook* states that: Var(\epsilon) = ...
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36 views

### Proportion of variance shared pairwise

I have several time series, structured into a matrix: dat = 1+(30-1).*rand(365,7); where each column refers to a different series of annual measurements. In my ...
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