The Stein Paradox in the Sense of the Pitman Measure of Closeness

Abstract

The dominance and related optimality properties of the usual Stein-rule or shrinkage estimators are typically developed for quadratic error loss functions. It is shown that under the classical Pitman closeness criterion the Stein-rule estimators possess a similar dominance property when the "closeness" measure is based on suitable quadratic norms.