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Simultaneous estimation of the multivariate normal mean under balanced loss function
Authors:Younshik Chung  Chansoo Kim
Institution:Department of Statistics , Pusan National University , Pusan, 609-735, Korea
Abstract:This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function which is defined as follows:

where 0 < w < 1 and for i = 1,…,p and j = 1,…,n, Xij is distributed as normal with mean θi and variance 1. It is shown that the sample mean, X, is admissible when p <3. For p ≥3, we obtain that James-Stein type estimator which has uniformly smaller risk than that of sample mean X.
Keywords:Admissibility  Inadmissibility  James-Stein type estimator
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