Convergence Rates of Empirical Bayes Estimation and Selection for Exponential Populations With Location Parameters

In this paper, we discuss the problems of empirical Bayes estimation for the exponential distributions with location parameters and the empirical Bayes rule for selecting the best of the exponential populations. We first derive the Bayes estimators and the Bayes selection rule and then construct empirical Bayes estimators for the location parameters and the empirical Bayes selection rule. Finally, we examine the asymptotic optimality properties of the proposed empirical Bayes estimators and the empirical Bayes selection rule.