Selection Procedures for Scale Parameters Using Two‐sample U‐statistics

Abstract

Summary Let be k independent populations having the same known quantile of order p (0 p 1) and let F(x)=F(x/i) be the absolutely continuous cumulative distribution function of the ith population indexed by the scale parameter 1, i = 1,…, k. We propose subset selection procedures based on two‐sample U‐statistics for selecting a subset of k populations containing the one associated with the smallest scale parameter. These procedures are compared with the subset selection procedures based on two‐sample linear rank statistics given by Gill & Mehta (1989) in the sense of Pitman asymptotic relative efficiency, with interesting results.