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A Note on Bootstrap for Gupta’s Subset Selection Procedure

Author

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  • Jun-ichiro Fukuchi

    (Gakushuin University)

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.

Suggested Citation

  • Jun-ichiro Fukuchi, 2020. "A Note on Bootstrap for Gupta’s Subset Selection Procedure," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 96-114, February.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:1:d:10.1007_s13171-019-00163-6
    DOI: 10.1007/s13171-019-00163-6
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    References listed on IDEAS

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    1. P. K. Kannan & Susan M. Sanchez, 1994. "Competitive Market Structures: A Subset Selection Analysis," Management Science, INFORMS, vol. 40(11), pages 1484-1499, November.
    2. William Horrace & Joseph Marchand & Timothy Smeeding, 2008. "Ranking inequality: Applications of multivariate subset selection," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(1), pages 5-32, March.
    3. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, October.
    4. William C. Horrace, 2006. "Selection Procedures for Economics," Applied Economics Quarterly (formerly: Konjunkturpolitik), Duncker & Humblot, Berlin, vol. 52(4), pages 357-374.
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