A Three-Stage Selection Procedure With an Exact Consistency

This article considers the problem of selecting the best population by using Bechhofer's indifference zone approach. Stein's two-stage procedure meets the probability requirement (exact consistency). However, it is shown that the procedure does not become asymptotically second-order efficient whatever the first sample sizes are chosen. Hall's three-stage procedure is asymptotically second-order efficient, but it loses the exact consistency. We propose a three-stage procedure that has an exact consistency and show that the procedure enjoys the asymptotic second-order efficiency.