IMPROVING ON THE JAMES-STEIN POSITIVE-PART ESTIMATOR

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 the ta 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 i mproves 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, h ave not previously been found; indeed, 1988 results of Beck and of Bro wn imply that no estimator dominating the positive-part estimator exis ts whose unbiased estimator of risk is uniformly smaller than that of the positive-part estimator.