부산대학교 도서관

Let $\theta_1,\theta_2,\cdots,\theta_k$ be parameters indexing $k$ populations and set $\theta_{[k]}=\max_{1\leq i\leq k}\theta_i$. It is shown how to construct simultaneous confidence intervals on $\theta_{[k]}-\theta_i,\;i=1,2,\cdots,k$. The technique rests on a theorem given herein which shows how to adapt any multiple comparison with control procedure (i.e., simultaneous confidence intervals for $\theta_j-\theta_i,\ i=1,2,\cdots,k,\ i\neq j)$ to the present problem. This represents an extension of work of Hsu [Ann. Statist. {\bf 9} (1981), no. 5, 1026--1034; MR0628758 (83b:62061)] in that neither independence of the samples nor normality is assumed, and it is not required that the sample sizes be equal or fixed. It is demonstrated that the proposed procedure compares favorably with various competitors in terms of interval length and coverage probabilities. Several examples are presented and relationships are noted to known ranking and selection procedures. \par \edref {The corrigenda consist of several corrections to formulas.}