Selecting the smallest normal variance through the comparisons of several likelihoods

Abstract

We are dealing with the problem of selecting the normal population having the smallest variance among k normal populations. We adopt "indifference zone approach" with a target value of the probability of correct selection P^∗. One may refer to Bechhofer et al (1968), Gibbons et al (1977) and Gupta and Panchapakesan (1979). We view this problem as a mutliple—hypothesis testing problem and we propose sequential tests which are shown to have a substantial "saving" in the average sample sizes compared to the corresponding well known fixed—sample size procedures. We suggest, however, two separate methods of defining the "saving" and work primarily with one of these notions. We consider some special cases of some or all of the population means being known. In the casesk =2 and k=3, we have presented extensive numerical results through simulations showing the merits (in almost all the simulations) of our proposed procedures. Also, for k= 2 we study various asymptotic behavior (as ) of the stopping time involved in our statistical methods, and these are summarized in theorems 1 and 2. Theorem 3 presents some partial asymptotic results (as ) in the case of k = 3.

Keywords:

• sequential multiple hypotheses testing
• fixed—sample rules
• saving
• asymptotic properties
• simulations and tables