On selecting the pareto-optimal subset of a class of populations

Abstract

Let P be a class of k populations (with k known) each having an underlying multivariate normal distribution with unknown mean vector. We suppose that the mean (vector) value of each population can be represented by a vector parameter with p components and use the notation M to denote the set of all mean vectors for these k populations. Independent samples of size n are drawn from each population in P. We say that a subset G of P of vectors is δ*-Pareto-optimal if no vector in M, differing in at least one component from some mean vector μ corresponding to a population in G, has the property that each of its components is larger by at least δ* > 0 than the corresponding component of the vector μ In this paper we evaluate procedures devised to select the δ*-Pareto-Optimal subset of a class of populations according to the minimum probability of correct selection over a region of the parameter space which we call the preference zone. For small values of k, theoretical calculations are given to analyze how big ...