The Performance of Some Sequential Procedures for a Ranking Problem

Abstract

Srivastava (1966) has proposed two classes of asymptotically efficient sequential procedures for selecting the population with the largest mean when nothing is assumed about the form of the distribution functions except for the finiteness of unknown variance. In order to choose between these two classes, it seems desirable to study the performance of these two classes of sequential procedures for moderate sample sizes. In this paper, assuming that these populations are normal, the average sample sizes and the error probabilities actually obtained are computed to compare the two procedures. Results of calculation show that Procedure B (see Section 2) is better than Procedure A in that the average sample size is smaller while the error probabilities are almost the same (the superiority of procedure B was suggested by Srivastava (1966) for a different intuitive reason). At the same time the calculation helps to show the closeness of the error probability (both cases) to $\alpha$. The calculation is on the lines of Ray (1957) and Robbins (1959) by generalizing a problem of the latter. Starr (1966) has recently carried out calculations to study the performance of a sequential procedure for finding fixed-width confidence bounds for the normal mean (see also Chow and Robbins, 1965).