Bounds on Reciprocal Moments with Applications and Developments in Stein Estimation and Post-Stratification

Abstract

SUMMARY Bounds on the kth reciprocal moment of a distribution are given in terms of the mean, variance and left extremity of the distribution. A methodology for obtaining distribution-specific bounds, with improved accuracy, is outlined. Some natural approximations are noted. Applications are given in Stein estimation, and in classical and Bayesian post-stratification.