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Nonparametric estimation and inference on conditional quantile processes

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  • Qu, Zhongjun
  • Yoon, Jungmo

Abstract

This paper presents estimation methods and asymptotic theory for the analysis of a nonparametrically specified conditional quantile process. Two estimators based on local linear regressions are proposed. The first estimator applies simple inequality constraints while the second uses rearrangement to maintain quantile monotonicity. The bandwidth parameter is allowed to vary across quantiles to adapt to data sparsity. For inference, the paper first establishes a uniform Bahadur representation and then shows that the two estimators converge weakly to the same limiting Gaussian process. As an empirical illustration, the paper considers a dataset from Project STAR and delivers two new findings.

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  • Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    • Handle: RePEc:eee:econom:v:185:y:2015:i:1:p:1-19
    DOI: 10.1016/j.jeconom.2014.10.008
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    Cited by:

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    2. Chiang, Harold D. & Hsu, Yu-Chin & Sasaki, Yuya, 2019. "Robust uniform inference for quantile treatment effects in regression discontinuity designs," Journal of Econometrics, Elsevier, vol. 211(2), pages 589-618.
    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. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    5. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly & Kaspar Wüthrich, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 123-137, January.
    6. Xu, Ke-Li, 2020. "Inference of local regression in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 218(2), pages 532-560.
    7. Valentina Corradi & Daniel Gutknecht, 2019. "Testing for Quantile Sample Selection," Papers 1907.07412, arXiv.org, revised Jan 2021.
    8. Zongwu Cai & Xiyuan Liu, 2020. "A Functional-Coefficient VAR Model for Dynamic Quantiles with Constructing Financial Network," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202017, University of Kansas, Department of Economics, revised Oct 2020.
    9. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    10. 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.
    11. 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.
    12. Manuel Arellano & Stéphane Bonhomme, 2016. "Nonlinear panel data estimation via quantile regressions," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 61-94, October.
    13. Yijian Huang, 2017. "Restoration of Monotonicity Respecting in Dynamic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 613-622, April.
    14. Racine, Jeffrey S. & Li, Kevin, 2017. "Nonparametric conditional quantile estimation: A locally weighted quantile kernel approach," Journal of Econometrics, Elsevier, vol. 201(1), pages 72-94.
    15. Liang Chen, 2019. "Nonparametric Quantile Regressions for Panel Data Models with Large T," Papers 1911.01824, arXiv.org, revised Sep 2020.
    16. Yingying DONG & Ying-Ying LEE & Michael GOU, 2019. "Regression Discontinuity Designs with a Continuous Treatment," Discussion papers 19058, Research Institute of Economy, Trade and Industry (RIETI).
    17. Zhongjun Qu & Jungmo Yoon, 2019. "Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 625-647, October.
    18. Chiang, Harold D. & Sasaki, Yuya, 2019. "Causal inference by quantile regression kink designs," Journal of Econometrics, Elsevier, vol. 210(2), pages 405-433.
    19. Karen X. Yan & Qi Li, 2018. "Nonparametric Estimation of a Conditional Quantile Function in a Fixed Effects Panel Data Model," JRFM, MDPI, vol. 11(3), pages 1-10, August.
    20. Haitian Xie, 2022. "Nonlinear and Nonseparable Structural Functions in Fuzzy Regression Discontinuity Designs," Papers 2204.08168, arXiv.org.

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    More about this item

    Keywords

    Nonparametric quantile regression; Uniform Bahadur representation; Uniform inference; Treatment effect;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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