The Annals of Statistics

Improving on the James-Stein Positive-Part Estimator

Peter Yi-Shi Shao and William E. Strawderman

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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

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

First available in Project Euclid: 11 April 2007

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Zentralblatt MATH identifier


Primary: 62C99: None of the above, but in this section
Secondary: 62F10: Point estimation 62H99: None of the above, but in this section

Minimaxity squared error loss location parameters


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.

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