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A note on the accuracy of bootstrap percentile method confidence intervals for a quantile

Author

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  • Hall, Peter
  • Martin, Michael A.

Abstract

It is shown that the bootstrap percentile method of constructing confidence intervals for quantiles is equivalent to the sign test method. As a result, and in contrast to many other problems, percentile-method intervals have coverage error of precise order n-1/2 in both one- and two-sided cases. We show that bootstrap iteration of percentile-method intervals has no role to play in quantile problems, and cannot be used to improve coverage accuracy. This is in marked distinction to more classical problems, where each iteration reduces the order of coverage error by the factor n-1/2 for one-sided intervals and n-1 for two-sided intervals. It thus emerges that standard bootstrap techniques perform poorly in constructing confidence intervals for quantiles: the percentile method is inaccurate for given levels, and produces nothing new; iteration of the percentile method fails completely; bias correction and accelerated bias correction are no more than adjustments to sign test intervals, and therefore fail; and percentile-t is hardly an efficacious alternative because of the non-availability of a suitable variance estimate.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:3:p:197-200
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    Cited by:

    1. David M. Kaplan & Lonnie Hofmann, 2019. "High-order coverage of smoothed Bayesian bootstrap intervals for population quantiles," Working Papers 1914, Department of Economics, University of Missouri, revised 19 Sep 2020.
    2. Hui Dong & Marvin K. Nakayama, 2017. "Quantile Estimation with Latin Hypercube Sampling," Operations Research, INFORMS, vol. 65(6), pages 1678-1695, December.
    3. Yijun Zuo, 2015. "Bahadur representations for bootstrap quantiles," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 597-610, July.

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