Empirical Bayes Procedures for Selecting the Best Population with Multiple Criteria

Consider k (k ≥ 2) populations whose mean θi and variance σi2 are all unknown. For given control values θ0 and σ02, we are interested in selecting some population whose mean is the largest in the qualified subset in which each mean is larger than or equal to θ0 and whose variance is less than or equal to σ02. In this paper we focus on the normal populations in details. However, the analogous method can be applied for the cases other than normal in some situations. A Bayes approach is set up and an empirical Bayes procedure is proposed which has been shown to be asymptotically optimal with convergence rate of order O(ln2n/n). A simulation study is carried out for the performance of the proposed procedure and it is found satisfactory.