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Bahadur representations for bootstrap quantiles

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  • Yijun Zuo

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. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Yijun Zuo, 2015. "Bahadur representations for bootstrap quantiles," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 597-610, July.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:5:p:597-610
    DOI: 10.1007/s00184-014-0517-5
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    References listed on IDEAS

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    1. Sen, Pranab Kumar, 1972. "On the Bahadur representation of sample quantiles for sequences of [phi]-mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 77-95, March.
    2. Hall, Peter & Martin, Michael A., 1989. "A note on the accuracy of bootstrap percentile method confidence intervals for a quantile," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 197-200, August.
    3. Athreya, K. B., 1983. "Strong law for the bootstrap," Statistics & Probability Letters, Elsevier, vol. 1(3), pages 147-150, March.
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