Comparisons of improved risk estimators of the multivariate mean vector

Abstract

The estimation of the mean vector of a multivariate normal distribution, under the uncertain prior information (UPI) that component means are equal but unknown, is considered. The positive part of Stein-Rule (PSE) and improved preliminary test (IPE) estimators are proposed. It is demonstrated analytically as well as computationally that the positive part of Stein-Rule estimator is superior to the usual Stein-Rule estimator (SE). Furthermore, it is shown that the proposed improved pretest estimator dominates the traditional preliminary test estimator (PE) regardless the correctness of the nonsample information. The relative dominance of the proposed estimators are presented analytically as well as graphically. Percentage improvements of the proposed estimators over the unrestricted estimator (UE) are computed. It is shown that for p ⩾ 3 , SE or PSE is the best to use while for p ⩽ 2 , UE is preferable.