On the performance of subset selection rules under normality

Abstract

From k normal populations N( θ 1, σ 1 2),…,N( θ k , σ k 2), where the means θ 1,…,θ k∈ R are unknown, and the variances σ 1 2,…, σ k 2>0 are known, independent random samples of sizes n 1,…, n k , respectively, are drawn. Based on these observations, a non-empty subset of these k populations of preferably small size has to be selected, which contains the population with the largest mean with a probability of at least P ∗ at every parameter configuration. Several subset selection rules which have been proposed in the literature are compared with Bayes selection rules for normal priors under two natural type of loss functions. Two new subset selection rules are considered.