Stein estimation: The spherically symmetric case

Abstract

This paper presents an expository development of Stein estimation with substantial emphasis on exact results for spherically symmetric distributions. The themes of the paper are: a) that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but expected from a variety of perspectives; b) that the amount of shrinkage allowable to preserve domination over the best invariant estimator is, when properly interpreted, relatively free from the assumption of normality; and c) that the potential savings in risk are substantial when accompanied by good quality prior information. © 1990, Institute of Mathematical Statistics. All Rights Reserved.