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A Note on Bootstrap for Gupta’s Subset Selection Procedure


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-order correct 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.

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The main part of this study is done while author is a visiting professor of University of Tokyo. The author would like to thank Professor Hiroshi Kurata for his hospitality. The author also wish to thank Professor Satoshi Kuriki and two anonymous referees for valuable suggestions and comments.

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Correspondence to Jun-ichiro Fukuchi.

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Fukuchi, Ji. A Note on Bootstrap for Gupta’s Subset Selection Procedure. Sankhya A 82, 96–114 (2020).

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Keywords and phrases

  • Bootstrap
  • Selection problem
  • Subset selection approach
  • Second-order correctness
  • Edgeworth expansion

AMS (2000) subject classification

  • Primary 62G09
  • Secondary 62F07