  In this paper, we consider the estimation of a mean vector of a multivariate
normal population where the mean vector is suspected to be nearly equal to mean
vectors of $k-1$ other populations. As an alternative to the preliminary test
estimator based on the test statistic for testing hypothesis of equal means, we
derive empirical and hierarchical Bayes estimators which shrink the sample mean
vector toward a pooled mean estimator given under the hypothesis. The
minimaxity of those Bayesian estimators are shown, and their performances are
investigated by simulation.
