  This paper is concerned with the simultaneous estimation of $k$ population
means when one suspects that the $k$ means are nearly equal. As an alternative
to the preliminary test estimator based on the test statistics for testing
hypothesis of equal means, we derive Bayesian and minimax estimators which
shrink individual sample means toward a pooled mean estimator given under the
hypothesis. It is shown that both the preliminary test estimator and the
Bayesian minimax shrinkage estimators are further improved by shrinking the
pooled mean estimator. The performance of the proposed shrinkage estimators is
investigated by simulation.
