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On copula-based conditional quantile estimators

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

Abstract

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

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    1. 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.
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    4. Noh, Hohsuk & El Ghouch, Anouar & Bouezmarni, Taoufik, 2013. "Copula-Based Regression Estimation and Inference," LIDAM Reprints ISBA 2013045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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, January.
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    11. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
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    1. Nasri, Bouchra R. & Rémillard, Bruno N. & Bouezmarni, Taoufik, 2019. "Semi-parametric copula-based models under non-stationarity," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 347-365.
    2. Hernández-Maldonado, Victor Miguel & Erdely, Arturo & Díaz-Viera, Martín & Rios, Leonardo, 2024. "Fast procedure to compute empirical and Bernstein copulas," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    3. Hamori, Shigeyuki & Motegi, Kaiji & Zhang, Zheng, 2020. "Copula-based regression models with data missing at random," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    4. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    5. Saeed Aldahmani & Othmane Kortbi & Mhamed Mesfioui, 2024. "Copula-Based Regression with Mixed Covariates," Mathematics, MDPI, vol. 12(22), pages 1-15, November.

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