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Sankhya A

pp 1–19 | Cite as

A Note on Bootstrap for Gupta’s Subset Selection Procedure

  • Jun-ichiro FukuchiEmail author
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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-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.

Keywords and phrases

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

AMS (2000) subject classification

Primary 62G09 Secondary 62F07 

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Notes

Acknowledgements

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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Copyright information

© Indian Statistical Institute 2019

Authors and Affiliations

  1. 1.Faculty of EconomicsGakushuin UniversityTokyoJapan

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