Bounds on reciprocal moments with applications and developments in Stein estimation and post-stratification. (English) Zbl 0603.62016

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.


62E10 Characterization and structure theory of statistical distributions
62D05 Sampling theory, sample surveys
62J07 Ridge regression; shrinkage estimators (Lasso)