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September, 1994 Improving on the James-Stein Positive-Part Estimator
Peter Yi-Shi Shao, William E. Strawderman
Ann. Statist. 22(3): 1517-1538 (September, 1994). DOI: 10.1214/aos/1176325640


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.


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Peter Yi-Shi Shao. William E. Strawderman. "Improving on the James-Stein Positive-Part Estimator." Ann. Statist. 22 (3) 1517 - 1538, September, 1994.


Published: September, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0820.62051
MathSciNet: MR1311987
Digital Object Identifier: 10.1214/aos/1176325640

Primary: 62C99
Secondary: 62F10, 62H99

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 3 • September, 1994
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