The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.
19
votes
0answers
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 ...
7
votes
0answers
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 ...
5
votes
0answers
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 ...
4
votes
0answers
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 ...
4
votes
0answers
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 ...
4
votes
0answers
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 ...
4
votes
0answers
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 ...
3
votes
0answers
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 ...
3
votes
0answers
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)} ...
3
votes
0answers
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) ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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. ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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?
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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 = ...
2
votes
0answers
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 ...
2
votes
0answers
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 ...
2
votes
0answers
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. ...
2
votes
0answers
383 views
2
votes
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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:
...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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
$$E(X^n)=\,?$$
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 $S_1 = (t_0, t_1, ..., t_m)$ ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
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) = ...
1
vote
0answers
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 ...
