### Improving on the James-Stein Positive-Part Estimator

Peter Yi-Shi Shao and William E. Strawderman
Source: Ann. Statist. Volume 22, Number 3 (1994), 1517-1538.

#### Abstract

The purpose of this paper is to give an explicit estimator dominating the positive-part James-Stein rule. The James-Stein estimator improves on the "usual" estimator $X$ of a multivariate normal mean vector $\theta$ if the dimension $p$ of the problem is at least 3. It has been known since at least 1964 that the positive-part version of this estimator improves on the James-Stein estimator. Brown's 1971 results imply that the positive-part version is itself inadmissible although this result was assumed to be true much earlier. Explicit improvements, however, have not previously been found; indeed, 1988 results of Bock and of Brown imply that no estimator dominating the positive-part estimator exists whose unbiased estimator of risk is uniformly smaller than that of the positive-part estimator.

First Page:
Primary Subjects: 62C99
Secondary Subjects: 62F10, 62H99
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aos/1176325640
JSTOR: links.jstor.org
Digital Object Identifier: doi:10.1214/aos/1176325640
Mathematical Reviews number (MathSciNet): MR1311987
Zentralblatt MATH identifier: 0820.62051