Artificially augmented samples, shrinkage, and mean squared error reduction

Abstract

An inequality is provided that determines when shrinkage reduces the mean squared error (MSE) of an unbiased estimate. Artificially augmented samples are then used to obtain, among others, shrinkage estimates of the population's variance and covariance, which improve the unbiased estimates for all parameter values and for all probability models with marginals having finite second moments, and alternative jackknife estimates that complement the usual jackknife estimates in reducing the MSE.