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

Wooff, David A.

J. R. Stat. Soc., Ser. B 47, 362-371 (1985).

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.

MSC:

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

Keywords:

regression shrinkage; Jensen’s inequality; recurrence relations; reciprocal moment; left extremity; distribution-specific bounds; Stein estimation; Bayesian post-stratification