On the performance of Gupta's subset selection rule

Abstract

Let X ¯ i ∼ N ( θ i , τ 2 / n ) , i = 1 , … , k , be independent sample means, based on a common sample size n from k normal populations with the same known variance τ 2 > 0 . To select a small non-empty subset that contains with a guaranteed probability P * the best population, i.e. the population associated with θ [ k ] = max { θ 1 , … , θ k } , Gupta [1956. On a decision rule for a problem in ranking means. Ph.D. Thesis, Mimeo, Series No. 150, Institute of Statistics, University of North Carolina, Chapel Hill; 1965. On some multiple decision (selection and ranking) rules. Technometrics 7, 225–245.] proposed and studied a subset selection rule that has become a classic and bears his name. Since then, its performance has been studied and compared with the performance of other subset selection rules by many authors. Gupta and Miescke [2002. On the performance of subset selection rules under normality. J. Statist. Plann. Inference 103, 101–115.] derived generalized Bayes rules under two loss functions and possibly unequal sample mean variances τ 2 / n i , i = 1 , … , k , but risk comparisons between these generalized Bayes rules and Gupta's classical rule appeared to be infeasible, both theoretically and numerically. With the advent of faster computers, risk comparisons via computer simulations have become feasible. Numerical results of this type for equal sample mean variances are presented in this paper.