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Calibrated interpolated confidence intervals for population quantiles

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  • Yvonne H. S. Ho
  • Stephen M. S. Lee

Abstract

Beran & Hall's (1993) simple linear interpolation provides a very convenient approach for constructing nonparametric confidence intervals for population quantiles based on a random sample of size n. We show that the coverage error of the interpolated interval, which is of order O(n-super- - 1), can be improved upon by calibrating the nominal coverage level. Three distinct methods of calibration are considered. The analytical and Monte Carlo methods succeed in reducing the order of coverage error to O(n-super- - 3/2), while the smoothed bootstrap method reduces it further to O(n-super- - 25/14).We provide guidelines for practical implementation of the calibration methods. Their performance is compared with the simple linear interpolated interval in a simulation study which confirms superiority of the calibrated intervals. Copyright 2005, Oxford University Press.

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  • Yvonne H. S. Ho & Stephen M. S. Lee, 2005. "Calibrated interpolated confidence intervals for population quantiles," Biometrika, Biometrika Trust, vol. 92(1), pages 234-241, March.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:1:p:234-241
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    File URL: http://hdl.handle.net/10.1093/biomet/92.1.234
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    Cited by:

    1. Jesse Frey & Yimin Zhang, 2017. "What Do Interpolated Nonparametric Confidence Intervals for Population Quantiles Guarantee?," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 305-309, October.
    2. Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.

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