Empirical Bayes Procedures for Selecting the Best Population with Multiple Criteria

Abstract

Consider k (k ≥ 2) populations whose mean θ _i and variance σ ² _i are all unknown. For given control values θ₀ and σ ² ₀ , 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 σ ² ₀ . 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(ln² n/n). A simulation study is carried out for the performance of the proposed procedure and it is found satisfactory.