Article

Title: A Note on Bootstrap for Gupta’s Subset Selection Procedure

Issue: Volume 82 Series A Part 1 Year 2020
Pages: 96 -- 114
Abstract
This study introduces a method of selecting a subset of k populations containing the best when the populations are ranked in terms of the population means. It is assumed that the populations have an unknown location family of distribution functions. The proposed method involves estimating the constant in Gupta’s subset selection procedure by bootstrap. It is shown that estimating this constant amounts to estimating the distribution function of a certain function of random variables. The proposed bootstrap method is shown to be consistent and second-ordercorrect in the sense that the accuracy of bootstrap approximation is better than that of the approximation based on limiting distribution. Results of a simulation study are given.
Primary 62G09; Secondary 62F07
Keywords and phrases: Bootstrap, Selection problem, Subset selection approach, Second-order correctness, Edgeworth expansion