A unified and generalized set of shrinkage bounds on minimax Stein estimates

Dominique Fourdrinier and William E. Strawderman

Journal of Multivariate Analysis, 2008, vol. 99, issue 10, 2221-2233

Abstract: Consider the problem of estimating the mean vector [theta] of a random variable X in , with a spherically symmetric density f(||x-[theta]||2), under loss ||[delta]-[theta]||2. We give an increasing sequence of bounds on the shrinkage constant of Stein-type estimators depending on properties of f(t) that unify and extend several classical bounds from the literature. The basic way to view the conditions on f(t) is that the distribution of X arises as the projection of a spherically symmetric vector (X,U) in . A second way is that f(t) satisfies (-1)jf(j)(t)>=0 for 0

Keywords: primary; 62C10; 62C20 Minimax estimators Quadratic loss Spherically symmetric distributions Location parameters Completely monotone functions Unimodality (search for similar items in EconPapers)
Date: 2008
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