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{1176325640,
author = {Shao, Peter Yi-Shi and Strawderman, William E.},
title = {Improving on the James-Stein Positive-Part Estimator},
journal = {Ann. Statist.},
volume = {22},
number = {1},
year = {1994},
pages = { 1517-1538},
language = {en},
url = {http://dml.mathdoc.fr/item/1176325640}
}
Shao, Peter Yi-Shi; Strawderman, William E. Improving on the James-Stein Positive-Part Estimator. Ann. Statist., Tome 22 (1994) no. 1, pp. 1517-1538. http://gdmltest.u-ga.fr/item/1176325640/