ASYMPTOTICALLY OPTIMAL RANKING AND SELECTION PROCEDURES
CORNELL UNIV ITHACA NY DEPT OF OPERATIONS RESEARCH
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Single-stage asymptotically optimal minimax procedures are developed for ranking populations in the presence of nuisance parameters, when the populations are ranked according to a parameter of the distribution and the so-called indifference-zone approach to ranking and selection problems is employed. This is accomplished by adapting methods used by Weiss and Wolfowitz for 2-decision tests of composite hypotheses problems in the presence of nuisance parameters to multiple-decision ranking and selection problems in the presence of nuisance parameters. For the problem of selecting the best population and for certain other ranking and selection goals, asymptotically optimal procedures are developed for situations in which the joint density function of the observations satisfies certain mild regularity conditions. In addition, the applicability of the basic method is demonstrated by developing asymptotically optimal procedures for ranking non-regular exponential and uniform distributions. The asymptotically optimal character of certain so-called natural selection procedures which already have been proposed in the literature is proved. Single-stage asymptotically optimal procedures are derived for certain problems for which heretofore no single-stage procedures had been proposed.
- Statistics and Probability
- Operations Research