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What Do Interpolated Nonparametric Confidence Intervals for Population Quantiles Guarantee?

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  • Jesse Frey
  • Yimin Zhang

Abstract

The interval between two prespecified order statistics of a sample provides a distribution-free confidence interval for a population quantile. However, due to discreteness, only a small set of exact coverage probabilities is available. Interpolated confidence intervals are designed to expand the set of available coverage probabilities. However, we show here that the infimum of the coverage probability for an interpolated confidence interval is either the coverage probability for the inner interval or the coverage probability obtained by removing the more likely of the two extreme subintervals from the outer interval. Thus, without additional assumptions, interpolated intervals do not expand the set of available guaranteed coverage probabilities.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:4:p:305-309
    DOI: 10.1080/00031305.2016.1226952
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    References listed on IDEAS

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    1. Derek S. Young & Thomas Mathew, 2014. "Improved nonparametric tolerance intervals based on interpolated and extrapolated order statistics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 415-432, September.
    2. 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.
    3. Hettmansperger, Thomas P. & Sheather, Simon J., 1986. "Confidence intervals based on interpolated order statistics," Statistics & Probability Letters, Elsevier, vol. 4(2), pages 75-79, March.
    4. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    5. Nyblom, Jukka, 1992. "Note on interpolated order statistics," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 129-131, May.
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    Cited by:

    1. Chaitra H. Nagaraja & Haikady N. Nagaraja, 2020. "Distribution‐free Approximate Methods for Constructing Confidence Intervals for Quantiles," International Statistical Review, International Statistical Institute, vol. 88(1), pages 75-100, April.

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