Bayesian subset selection for additive and linear loss function

Given k independent samples of common size n from k populations πj,…,πk with distribution the problem is to select a non-empty subset form {πj,…,πk}, which is associated with "good" (large) θ-values. We consider this problem from a Bayesian approach. By choosing additive and especially linear loss functions we try to fill a gap lying in between the results of Deely and Gupta (1968) and more recent papers due to Goel and Rubin (1977), Gupta and Hsu (1978) and other authors. It is shown that under acertain "normal model" Seal's procedure turns out to be Bayes w.r.t. an unrealistic loss function where as Gupta's maximunl means procedure turns out to be ( for large n) asymptotically Bayes w.r. …