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Optimal smoothing in nonparametric conditional quantile derivative function estimation

Author

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  • Lin, Wei
  • Cai, Zongwu
  • Li, Zheng
  • Su, Li

Abstract

Marginal effect in nonparametric quantile regression is of special interest as it quantitatively measures how one unit change in explanatory variable heterogeneously affects dependent variable ceteris paribus at distinct quantiles. In this paper, we propose a data-driven bandwidth selection procedure based on the gradient of an unknown quantile regression function. Our method delivers the bandwidth with the oracle property in the sense that it is asymptotically equivalent to the optimal bandwidth if the true gradient were known. The results of Monte Carlo simulations are reported, and the finite sample performance of our proposed method confirms our theoretical analysis. An empirical application is also provided, showing that our proposed method delivers more reasonable and reliable quantile derivative estimates than traditional cross validation method.

Suggested Citation

  • Lin, Wei & Cai, Zongwu & Li, Zheng & Su, Li, 2015. "Optimal smoothing in nonparametric conditional quantile derivative function estimation," Journal of Econometrics, Elsevier, vol. 188(2), pages 502-513.
    • Handle: RePEc:eee:econom:v:188:y:2015:i:2:p:502-513
    DOI: 10.1016/j.jeconom.2015.03.014
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    as
    1. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
    2. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    3. Anglin, Paul M & Gencay, Ramazan, 1996. "Semiparametric Estimation of a Hedonic Price Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 633-648, Nov.-Dec..
    4. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    5. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    6. Xiao, Zhijie, 2009. "Quantile cointegrating regression," Journal of Econometrics, Elsevier, vol. 150(2), pages 248-260, June.
    7. Xia, Yingcun & Li, W. K., 2002. "Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 265-287, November.
    8. Qi Li & Jeffrey Scott Racine, 2006. "Density Estimation, from Nonparametric Econometrics: Theory and Practice," Introductory Chapters, in: Nonparametric Econometrics: Theory and Practice, Princeton University Press.
    9. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    10. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    11. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    12. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    13. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    14. Daniel J. Henderson & Christopher F. Parmeter & Subal C. Kumbhakar, 2007. "Nonparametric estimation of a hedonic price function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 695-699.
    15. Lin, Zhengyan & Li, Degui, 2007. "Asymptotic normality for L1-norm kernel estimator of conditional median under association dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1214-1230, July.
    16. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    17. Buchinsky, Moshe, 1994. "Changes in the U.S. Wage Structure 1963-1987: Application of Quantile Regression," Econometrica, Econometric Society, vol. 62(2), pages 405-458, March.
    18. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    19. Wolfgang Härdle & Philippe Vieu, 1992. "Kernel Regression Smoothing Of Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 209-232, May.
    20. Victor Chernozhukov & Christian Hansen, 2004. "The Effects of 401(K) Participation on the Wealth Distribution: An Instrumental Quantile Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 735-751, August.
    21. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    22. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
    23. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
    24. Henderson, Daniel J. & Li, Qi & Parmeter, Christopher F. & Yao, Shuang, 2015. "Gradient-based smoothing parameter selection for nonparametric regression estimation," Journal of Econometrics, Elsevier, vol. 184(2), pages 233-241.
    25. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    26. Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 333-346, September.
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    3. 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.

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    More about this item

    Keywords

    Gradient estimation; Local polynomial smoothing; Lease squares cross validation; Quantile regression;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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