Selecting the Population Most Close to a Control via Empirical Bayes Approach

Abstract

This article deals with the problem of selecting the population most equivalent to a control from among k independent normal populations using the parametric empirical Bayes approach. By combining useful information from the past data, an empirical Bayes selection procedure is studied. It is proved that the regret of converges to zero at a rate , where n is the number of past observations at hand. A simulation study is carried out to investigate the performance of for small to moderate values of n.

Keywords:

• Asymptotically optimal
• Bayes selection procedure
• Empirical Bayes
• Equivalent to a control
• Rate of convergence
• Regret

Mathematics Subject Classification:

• Primary 62F07
• Secondary 62C12, 62C10

Acknowledgment

We are grateful to a referee whose careful reading and helpful comments led to an improvement in this presentation. This article was partially supported by grant NSC95-2118-M-032-014 of NSC, Taiwan, Republic of China.