Optimal designs for variance function estimation using sample variances

Accounting for Multi - stage Sample Designs in Complex Sample Variance

Nationally representative samples of large populations often have complex design features for a variety of reasons (e.g., cost efficiency). For purposes of estimating sampling variances based on complex multi-stage sample designs involving stratification and cluster sampling, the sampling error codes provided by survey organizations in public use survey data files often assume “ultimate cluster...

Variance adaptive shrinkage (vash): flexible empirical Bayes estimation of variances

MOTIVATION Genomic studies often involve estimation of variances of thousands of genes (or other genomic units) from just a few measurements on each. For example, variance estimation is an important step in gene expression analyses aimed at identifying differentially expressed genes. A common approach to this problem is to use an Empirical Bayes (EB) method that assumes the variances among gene...

Optimal variance estimation without estimating the mean function

We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean squared differences of these paired observations on the squared distances between paired covariates via a simple least squares procedure, the resulting varianc...

Estimation of Process Variances in Robust Parameter Designs

Improved variance estimation along sample eigenvectors

Second order statistics estimates in the form of sample eigenvalues and sample eigenvectors give a sub optimal description of the population density. So far only attempts have been made to reduce the bias in the sample eigenvalues. However, because the sample eigenvectors differ from the population eigenvectors as well, the population eigenvalues are biased estimates of the variances along the ...