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On copula-based conditional quantile estimators


  • Rémillard, Bruno
  • Nasri, Bouchra
  • Bouezmarni, Taoufik


Recently, two different copula-based approaches have been proposed to estimate the conditional quantile function of a variable Y with respect to a vector of covariates X: the first estimator is related to quantile regression weighted by the conditional copula density, while the second estimator is based on the inverse of the conditional distribution function written in terms of margins and the copula. Using empirical processes, we show that even if the two estimators look quite different, their estimation errors have the same limiting distribution. Also, we propose a bootstrap procedure for the limiting process in order to construct uniform confidence bands around the conditional quantile function.

Suggested Citation

  • Rémillard, Bruno & Nasri, Bouchra & Bouezmarni, Taoufik, 2017. "On copula-based conditional quantile estimators," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 14-20.
  • Handle: RePEc:eee:stapro:v:128:y:2017:i:c:p:14-20
    DOI: 10.1016/j.spl.2017.04.014

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    References listed on IDEAS

    1. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    2. V. Chavez-Demoulin & A. C. Davison, 2005. "Generalized additive modelling of sample extremes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 207-222.
    3. Hohsuk Noh & Anouar El Ghouch & Taoufik Bouezmarni, 2013. "Copula-Based Regression Estimation and Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 676-688, June.
    4. Hohsuk Noh & Anouar El Ghouch & Ingrid Van Keilegom, 2015. "Semiparametric Conditional Quantile Estimation Through Copula-Based Multivariate Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 167-178, April.
    5. Eric Bouyé & Mark Salmon, 2009. "Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 721-750.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, October.
    7. Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2016. "Bernstein estimation for a copula derivative with application to conditional distribution and regression functionals," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 351-374, June.
    8. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    9. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    10. Bouezmarni Taoufik & Ghouch El & Taamouti Abderrahim, 2013. "Bernstein estimator for unbounded copula densities," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 343-360, December.
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