Bachhofer-Gupta-Sobel Memorial Symposium on
Ranking and Selection and Multiple Comparison Procedures Methodologies

Higher Than Second-Order Approximations Via Two-Stage Sampling for Selecting from Folded Normal Populations

We consider a problem for selecting from normal populations the one with the largest absolute mean under the indifference-zone formulation of Bechhofer (1954). When the common variance is assumed known, Rizvi (1971) had proposed a single-stage procedure. We assume, however, that the normal populations have a common but unknown variance. Hence, no single-stage procedure that guarantees a preassigned probability of correct selection (PCS) will exist. We investigate a two-stage procedure analogous to that of Jeyaratnam and Panchapakesan (1998). We proceed to develop various asymptotic characteristics of such two-stage selection procedures up to and beyond second-order. The asymptotic analyses so developed hold quite generally for pursuing higher than second-order optimality of two-stage sampling. In this investigation, we primarily focus on both the average sample size and PCS.