On a best-choice problem by dependent criteria

Abstract

We study the problem of maximizing the probability of stopping at an object which is best in at least one of a given set of criteria, using only stopping rules based on the knowledge of whether the current object is relatively best in each of the criteria. The asymptotic results for the case of independent criteria are shown to hold in certain cases where the componentwise maxima are, pairwise, either asymptotically independent or asymptotically full dependent.An example of the former is a random sample from a bivariate correlated normal distribution; thus our results settle a question posed recently by T. S. Ferguson.