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A note on coverage error of bootstrap confidence intervals for quantiles

Published online by Cambridge University Press:  24 October 2008

D. De Angelis ,
Peter Hall  and
G. A. Young
D. De Angelis
Affiliation:
University of Rome, ‘La Sapienza’
Peter Hall
Affiliation:
CMA, Australian National University
G. A. Young
Affiliation:
DPMMS, 16 Mill Lane, Cambridge
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Abstract

An interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of size n−½, where n denotes sample size. By way of contrast, the error would be O(n−1) for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved to o(n−½) by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage error O(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-t are also analysed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 3 , November 1993 , pp. 517 - 531
Copyright
Copyright © Cambridge Philosophical Society 1993

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