Some notes on improving upon the James-Stein estimator

Abstract

We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of smooth estimators parameterized by \alpha dominating the James-Stein estimator. The estimator for \alpha=1 corresponds to the generalized Bayes estimator with respect to the harmonic prior. When \alpha goes to infinity, the estimator converges to the James-Stein positive-part estimator. Thus the class of our estimators is a bridge between the admissible estimator (\alpha=1) and the inadmissible estimator (\alpha=\infty). Although the estimators have quasi-admissibility which is a weaker optimality than admissibility, the problem of determining whether or not the estimator for \alpha>1 admissible is still open.