A Two-Stage Procedure for Selecting the Largest Mean Based on Conditional Probability Analysis

Abstract

SYNOPTIC ABSTRACTThis paper follows the spirit of the conditional approach due to Kiefer in which procedures for selecting the best population or subset containing the best population are evaluated by conditional measures of loss. We construct a two-stage procedure to select the best population or subset containing the best population which satisfies a double probability requirement; the (conditional) probabilities of correct selection for μ in the preference and indifference zones are each separately bounded below by given preassigned constants. Many users of ranking and selection point out that there is no strong probability inequality or lower bound on the PCS that can be made when the parameters are in the indifference zone and they regard this as a criticism of ranking and selection in general. The aim in this paper is to offset any such criticism by providing lower bounds for the probability of a correct selection in both the indifference and the preference zones.