Selection Procedures for Location Parameters Based on Two-Sample U-Statistics

Abstract

Let π1, ... , πk be k independent populations and let Fi ( x)= F( x - θi) be the absolutely continuous cumulative distribution function (cdf) of the i-th population indexed by the location parameter θi; i=1,,.... k. A class of subset selection procedures based on sub-sample extrema for unequal sample sizes is proposed for the problem of selecting a subset from ( π1, .... πk) which contains the population with largest location parameter. The proposed subset selection procedures are then compared with the subset selection procedures of Hsu (1981) in the sense of Pitman ARE (asymptotic relative efficiency). It is shown that these procedures can approximately be implemented with the help of existing tables and sample size sufficient for their implementation, based on simulation results, is discussed. AMS (1980) Subject Classification: Primary 62F07; Secondary 62H10