BAYESIAN SUBSET SELECTION FOR ADDITIVE AND LINEAR LOSS FUNCTIONS

Given k independent samples of common size n from k populations n1 with distributions PQ, (K 6 lie IR, i = lk, the problem is to select a non-empty subset S(X-j. xr) from {tt-j, s’ which is associated with “good11 (large) d-values. We consider this problem from a Bayesian approach. By choosing additive (L(0, s) = £ L.(e)) and especially linear i £s (L(o, s) = y (or,-0.-e)) 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 a certain “normal model” Seal's procedure turns out to be Bayes w.r.t. an unrealistic loss function whereas Gupta's maximum means procedure turns out to be (for large n) asymptotically Bayes w.r.t. more realistic additive loss functions. Finally, in the appendix some bounds for E(max (y.+pV.)) j=l, k are derived (where u 6 IfA, p 6 IR are fixed known and VN(0,1)) to approximate the Bayes rules w.r.t. linear loss functions in cases where n is finite. © 1979, Taylor & Francis Group, LLC. All rights reserved.