Resumen
Consider k(k?2) normal populations whose mean ?i and variance si2 are all unknown. Let ?i be some function of ?i and si2 and ?i is the parameter of main interest. For given control values ?0 and s02, we want to select some population whose associated value of ?i the largest and also it is larger than ?0 and whose associated variance is less than or equal to s02. An empirical Bayes selection rule is proposed which has been shown to be asymptotically optimal with convergence rate of order O((lnN)2/N), where N is the minimum number of past observations at hand in each population. A simulation study is also carried out for the performance of the proposed empirical Bayes selection rule, and it is found satisfactory.