On a shrinkage estimator of a normal common mean vector

The problem of estimating the p - 1 mean vector [theta] based on two independent normal vectors Y1 ~ Np([theta], [sigma]2I) and Y2 ~ Np([theta], [xi][sigma]2I) is considered. For p >= 3, when [xi] and [sigma]2 are unknown, it was shown by George (1991, Ann. Statist.) that under certain conditions estimators of the form [delta][eta] = [eta]Y1 + (1 - [eta])Y2, where [eta] is a fixed number in (0, 1), are uniformly dominated by a shrinkage estimator under the squared error loss. In this paper, George's result is improved by obtaining a simpler and better condition for the domination.