Parametric Empirical Bayes Rules for Selecting the Most Probable Multinomial Event

摘要

This document considers a multinominal population with k (> or = 2) cells and an associated probability vector. A cell associated with p(k) is called the most probable event. We are interested in selecting the most probable event. Let i denote the index of the selected cell. Under a loss function this statistical selection problem is studied via a parametric empirical Bayes approach. Two empirical Bayes selection rules are proposed. They are shown to be asymptotically optimal at least of order 0(exp(-c sub 1n)) for some positive constants c sub i = 1,2, where n is the number of accumulated past experience (observations) at hand.