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Nonparametric conditional quantile estimation: A locally weighted quantile kernel approach

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  • Racine, Jeffrey S.
  • Li, Kevin

Abstract

Nonparametric conditional cumulative distribution function (CDF) estimation has emerged as a powerful tool having widespread potential application, which has led to a literature on estimators of conditional quantile functions that are obtained via inversion of the nonparametrically estimated conditional CDF. Other nonparametric estimators of conditional quantiles that are based on an alternative characterization of the quantile (i.e., as the function that minimizes the expectation of the check-function) have also appeared in the literature. In this paper, we propose a novel nonparametric approach. Relative to its inverse-CDF-based and the check-function-based peers, our proposed estimator has a simple expression. We also show that under certain conditions, our estimator is more efficient in tail regions when the data has unbounded support (our theoretical results underscore this property). Theoretical underpinnings are developed, a method for data-driven smoothing parameter selection is provided, and Monte Carlo simulations and empirical examples are considered. Two empirical examples illustrate how the proposed approach can deliver more reasonable quantile and quantile derivative estimates than its inverse-CDF-based and the check-function-based counterparts, particularly in tail regions.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:201:y:2017:i:1:p:72-94
    DOI: 10.1016/j.jeconom.2017.06.020
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    Cited by:

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    2. Fahimah A. Al-Awadhi & Zoulikha Kaid & Ali Laksaci & Idir Ouassou & Mustapha Rachdi, 2019. "Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 217-240, June.
    3. Laurent Gardes & Armelle Guillou & Claire Roman, 2020. "Estimation of extreme conditional quantiles under a general tail-first-order condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 915-943, August.
    4. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    5. Chen, Xirong & Li, Degui & Li, Qi & Li, Zheng, 2019. "Nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates," Journal of Econometrics, Elsevier, vol. 212(2), pages 433-450.
    6. Emmanuel Torsen & Peter N. Mwita & Joseph K. Mung’atu, 2019. "A Three-Step Nonparametric Estimation of Conditional Value-At-Risk Admitting a Location-Scale Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(4), pages 1-1.
    7. Wang, Qiao, 2023. "A simple nonparametric conditional quantile estimator for time series with thin tails," Economics Letters, Elsevier, vol. 232(C).
    8. Mickaël De Backer & Anouar El Ghouch & Ingrid Van Keilegom, 2020. "Linear censored quantile regression: A novel minimum‐distance approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1275-1306, December.

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    More about this item

    Keywords

    Kernel smoothing; Quantile Kernel function;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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