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Fractional order statistic approximation for nonparametric conditional quantile inference

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  • Goldman, Matt
  • Kaplan, David M.

Abstract

Using and extending fractional order statistic theory, we characterize the O(n−1) coverage probability error of the previously proposed (Hutson, 1999) confidence intervals for population quantiles using L-statistics as endpoints. We derive an analytic expression for the n−1 term, which may be used to calibrate the nominal coverage level to get O(n−3/2[log(n)]3) coverage error. Asymptotic power is shown to be optimal. Using kernel smoothing, we propose a related method for nonparametric inference on conditional quantiles. This new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations. Code is provided for both unconditional and conditional inference.

Suggested Citation

  • Goldman, Matt & Kaplan, David M., 2017. "Fractional order statistic approximation for nonparametric conditional quantile inference," Journal of Econometrics, Elsevier, vol. 196(2), pages 331-346.
    • Handle: RePEc:eee:econom:v:196:y:2017:i:2:p:331-346
    DOI: 10.1016/j.jeconom.2016.09.015
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    Cited by:

    1. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    2. 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.
    3. Matt Goldman & David M. Kaplan, 2018. "Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 136-169, June.
    4. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    5. Alan Hutson, 2018. "Comment on “What Do Interpolated Nonparametric Confidence Intervals for Population Quantiles Guarantee?”, Frey and Zhang (2017)," The American Statistician, Taylor & Francis Journals, vol. 72(3), pages 302-302, July.
    6. Goldman, Matt & Kaplan, David M., 2018. "Comparing distributions by multiple testing across quantiles or CDF values," Journal of Econometrics, Elsevier, vol. 206(1), pages 143-166.
    7. 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.
    8. David M. Kaplan, 2014. "Nonparametric Inference on Quantile Marginal Effects," Working Papers 1413, Department of Economics, University of Missouri.

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    More about this item

    Keywords

    Dirichlet; High-order accuracy; Inference-optimal bandwidth; Kernel smoothing;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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