## The Annals of Statistics

- Ann. Statist.
- Volume 22, Number 3 (1994), 1517-1538.

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

Peter Yi-Shi Shao and William E. Strawderman

#### 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.

#### Article information

**Source**

Ann. Statist., Volume 22, Number 3 (1994), 1517-1538.

**Dates**

First available in Project Euclid: 11 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176325640

**Digital Object Identifier**

doi:10.1214/aos/1176325640

**Mathematical Reviews number (MathSciNet)**

MR1311987

**Zentralblatt MATH identifier**

0820.62051

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62C99: None of the above, but in this section

Secondary: 62F10: Point estimation 62H99: None of the above, but in this section

**Keywords**

Minimaxity squared error loss location parameters

#### Citation

Shao, Peter Yi-Shi; Strawderman, William E. Improving on the James-Stein Positive-Part Estimator. Ann. Statist. 22 (1994), no. 3, 1517--1538. doi:10.1214/aos/1176325640. https://projecteuclid.org/euclid.aos/1176325640