SOME COMMENTS ON 2-STAGE SELECTION PROCEDURES

In this paper we study the procedures of Dudewicz and Dalai (1975), and the modifications suggested by Rinott (1978), for selecting the largest mean from k normal populations with unknown variances. We look at the case k = 2 in detail, because there is an optimal allocation scheme here. We do not really allocate the total number of samples into two groups, but we estimate this optimal sample size, as well, so as to guarantee the probability of correct selection (written as P(CS)) at least P, 1/2 < P < 1. We prove that the procedure of Rinott is “asymptotically in-efficient” (to be defined below) in the sense of Chow and Robbins (1965) for any k > 2. Next, we propose two-stage procedures having all the properties of Rinott's procedure, together with the property of “asymptotic efficiency” - which is highly desirable. © 1979 Taylor & Francis Group, LLC. All rights reserved.