Performance of Subset Selection Procedures Under Normality

摘要

From k normal populations N(t1,t1(2)),...,N(tk,tk(2)), where the means t1, ,tk in R are unknown, and the variances t1(2),...,tk(2) > 0 are known, independent random samples of sizes n1,...,nk, 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 probability of the lest P(*) at every parameter configuration. Several subset selection procedures which have been proposed in the literature are compared with Bayes selection procedures for normal priors under two natural type of loss functions. Two new subset selection procedures are considered.