On a Sequential Subset Selection Procedure for Exponential Family Distributions

Abstract

Abstract : The paper deals with the problem of selecting the best population among k populations belonging to the same class of exponential family distributions through sequential subset selection approach. We desire that the best population should be selected and each selected population should be good. Based on the modified likelihood ratio of the conditional frequency function of some statistics, an elimination-type sequential subset selection procedure is proposed. This sequential procedure achieves the selection goal with guaranteed probability at least P* for some prespecified value P*. At each stage, this procedure also provides some statistical inference about an upper bound on the measure of separation from the unknown best population of each remaining contending population. Finally, a modified sequential procedure to select a good population is also studied. This modified sequential procedure achieves the goal of selecting a good population with guaranteed at least P*.