# Tagged Questions

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

789 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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### 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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### Bound for Arithmetic Harmonic mean inequality for matrices?

NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ...
153 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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### How to test whether mean and variance is the same in two small samples?

I would like to test two relatively small samples against the null hypothesis that both their means and variances are the same. The alternative would be that they in fact differ. I saw a post on this ...
241 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 ...
86 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 ...
289 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) ...
188 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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### Variance of a difference in marginal proportions in a three-way contingency table

Let a multivariate distribution be given by $P(Y,S_1,S_2)$, where all three variables are discrete, $Y$ is multivalued, $S_1=(0,1)$ and $S_2=(0,1)$, respectively, and all may be dependent. Define the ...
73 views

### Graphical representation of variance

I'm learning statistics and I can imagine pretty well what the standard deviation looks like (image here). But, knowing that the standard deviation is the square root of the variance, I just can't ...
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### Variance of sample mean of bootstrap sample

Let $X_{1},...,X_{n}$be distinct observations (no ties). Let $X_{1}^{*},...,X_{n}^{*}$denote a bootstrap sample (a sample from the empirical CDF) and let ...
48 views

### t-test on two variance calculations

I have survey data that was recorded in a many different towns. I want to see for which variables is the data significantly more or less variable within towns than across all towns. Currently, I'm ...
32 views

### Index of dispersion with approximate distribution

I have an unknown discrete probability distribution $D$ ($D$ is a probability mass function), defined on an interval $[a,b]$ ($a>0$) and an estimation $\hat{D}$ such that, for all $t\in[a,b]$, ...
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### Calculation of variance in boundary cases of constrained likelihood

I am computing the MLE values of some parameters of a likelihood function, subject to non-negativity constraints. Given these constraints, some of the MLE values for my parameters are exactly in the ...
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### Is there a one-tailed test for difference in data variance in a mixed model?

I would like to test if the variation of my response variable is higher for one level of an explanatory variable than for the other. However I am not interested in the total variation, but only ...
40 views

### Is the following property for positive random variables fulfilled in general?

[I have cross-posted this from math.stackexchange: http://math.stackexchange.com/questions/476466/is-the-following-property-for-positive-random-variables-fulfilled-in-general ] Suppose we have a ...
252 views

### How to normalize data prior to computation of covariance matrix

In all my self-study, I have come across many different ways in which people seem to normalize their data, prior to the computation of the covariance matrix. I am confused as to what ways are ...
45 views

### Variance in a known population

I am working on a problem that is similar to the standard radioactive decay rate experiment, but with a twist. In the normal experiment, one takes several different measurements of the decay rate, ...
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### Measuring parameter sensitivity and variability (standard-error) in k-fold cross-validation

I mainly use k-fold cross-validation for parameter tuning and model selection for prediction problems. Now, is there a standard or if not a less-known way to measure the sensitivity of the parameters ...
51 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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### 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 ...
58 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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### 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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### 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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### 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. ...
225 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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### 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 ...
112 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 ...
157 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 ...
346 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 ...
127 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 ...
304 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 ...
172 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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### 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 ...