Simultaneous estimation of the multivariate normal mean under balanced loss function

This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function which is defined as follows: [GRAPHICS] where 0 < w < 1 and for i = 1,...,p and j = 1,..., n, X-ij is distributed as normal with mean theta(i) and variance 1. It is shown that the sample mean, <( X)over bar>, is admissible when p < 3. For p greater than or equal to 3, we obtain that James-Stein type estimator which has uniformly smaller risk than that of sample mean (X) over bar.