The multinomial selection problem

Abstract

In this thesis, we study indifference-zone multinomial selection procedures, thatis, procedures for selecting the most probable (?best?) multinomial cell. Such procedureshave a number of real-world applications ? for instance, which is the mostpopular television show in a particular time slot, or which manufacturing strategyhas the highest probability of yielding the largest profit on a particular trial? Theindifference-zone procedures we examine all satisfy a probability requirement thatguarantees to correctly select with high probability the best multinomial categoryunder a variety of underlying probability configurations. We show by Monte Carloand exact calculations that certain sequential sampling procedures perform betterthan others. We also offer various extensions and thoughts for future research.1