Among k(greater-than-or-equal-to 2) exponential populations with location parameters, we use the Empirical Bayes approach to select the best population. We first construct estimators for the unknown prior distribution. Then, the Bayes selection rule d(n) with respect to the estimated prior distribution is considered as the proposed empirical Bayes selection rule. We show the consistency of the estimated prior distribution and establish the asymptotic optimality of the rule d(n). Finally we give an illustrative example to implement the proposed procedure.
