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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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    References listed on IDEAS

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    1. David M. Kaplan & Matt Goldman, 2011. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1503, Department of Economics, University of Missouri, revised 21 Nov 2016.
    2. Yao, Qiwei & Polonik, Wolfgang, 2002. "Set-indexed conditional empirical and quantile processes based on dependent data," LSE Research Online Documents on Economics 5878, London School of Economics and Political Science, LSE Library.
    3. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    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. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
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    8. David M. Kaplan & Matt Goldman, 2013. "Comparing distributions by multiple testing across quantiles," Working Papers 13-19, Department of Economics, University of Missouri, revised Feb 2018.
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    Cited by:

    1. David M. Kaplan & Matt Goldman, 2013. "Comparing distributions by multiple testing across quantiles," Working Papers 13-19, Department of Economics, University of Missouri, revised Feb 2018.
    2. David M. Kaplan & Matt Goldman, 2011. "Nonparametric inference on conditional quantile differences and linear combinations, using L-statistics," Working Papers 1620, Department of Economics, University of Missouri, revised 21 Nov 2016.
    3. Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    4. David M. Kaplan, 2014. "Nonparametric Inference on Quantile Marginal Effects," Working Papers 1413, Department of Economics, University of Missouri.

    More about this item

    Keywords

    Dirichlet; High-order accuracy; Inference-optimal bandwidth; Kernel smoothing;

    JEL classification:

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

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