The Annals of Statistics

Improving on the James-Stein Positive-Part Estimator

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

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