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Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion

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  • Kaplan, David M.

Abstract

To estimate a sample quantile’s variance, the quantile spacing method involves smoothing parameter m. When m,n→∞, the corresponding Studentized test statistic is asymptotically N(0,1). Holding m fixed instead, the asymptotic distribution contains the Edgeworth expansion term capturing the variance of the quantile spacing. Consequently, the fixed-m distribution is more accurate than the standard normal under both asymptotic frameworks. A testing-optimal m is proposed to maximize power subject to size control. In simulations, the new method controls size better than similar methods while maintaining good power. Throughout are results for two-sample quantile treatment effect inference. Code is available online.

Suggested Citation

  • Kaplan, David M., 2015. "Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion," Journal of Econometrics, Elsevier, vol. 185(1), pages 20-32.
    • Handle: RePEc:eee:econom:v:185:y:2015:i:1:p:20-32
    DOI: 10.1016/j.jeconom.2014.08.011
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    Cited by:

    1. 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.
    2. 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.
    3. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "A robust confidence interval of historical Value-at-Risk for small sample," Documents de travail du Centre d'Economie de la Sorbonne 16034, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. 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.
    5. David M. Kaplan, 2014. "Nonparametric Inference on Quantile Marginal Effects," Working Papers 1413, Department of Economics, University of Missouri.
    6. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01317391, HAL.
    7. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "Capturing the intrinsic uncertainty of the VaR: Spectrum representation of a saddlepoint approximation for an estimator of the VaR," Documents de travail du Centre d'Economie de la Sorbonne 16034r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2016.

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    More about this item

    Keywords

    Fixed-smoothing; High-order accuracy; Hypothesis testing; Testing-optimal smoothing parameter;
    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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