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Bahadur representations for bootstrap quantiles

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Abstract

A bootstrap sample may contain more than one replica of original data points. To extend the classical Bahadur type representations for the sample quantiles in the independent identical distributed case to bootstrap sample quantiles therefore is not a trivial task. This manuscript fulfils the task and establishes the asymptotic theory of bootstrap sample quantiles.

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Acknowledgments

The Author thanks two referees for their helpful and constructive comments and suggestions. Thanks go to his former RA Juan Du for the initial 13 pages Latex typing (http://www.stt.msu.edu/~zuo/papers_html/bahadurciold.dvi). The research was partially supported by NSF Grants DMS-0234078 and DMS-0501174.

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Authors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, East Lansing, MI, 48824, USA

    Yijun Zuo

  2. School of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, Jiangxi, China

    Yijun Zuo

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  1. Yijun Zuo
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Correspondence to Yijun Zuo.

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Zuo, Y. Bahadur representations for bootstrap quantiles. Metrika 78, 597–610 (2015). https://doi.org/10.1007/s00184-014-0517-5

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  • DOI: https://doi.org/10.1007/s00184-014-0517-5

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