Electronic Journal of Statistics

Semiparametric copula quantile regression for complete or censored data

Mickaël De Backer, Anouar El Ghouch, and Ingrid Van Keilegom

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When facing multivariate covariates, general semiparametric regression techniques come at hand to propose flexible models that are unexposed to the curse of dimensionality. In this work a semiparametric copula-based estimator for conditional quantiles is investigated for both complete or right-censored data. In spirit, the methodology is extending the recent work of Noh, El Ghouch and Bouezmarni [34] and Noh, El Ghouch and Van Keilegom [35], as the main idea consists in appropriately defining the quantile regression in terms of a multivariate copula and marginal distributions. Prior estimation of the latter and simple plug-in lead to an easily implementable estimator expressed, for both contexts with or without censoring, as a weighted quantile of the observed response variable. In addition, and contrary to the initial suggestion in the literature, a semiparametric estimation scheme for the multivariate copula density is studied, motivated by the possible shortcomings of a purely parametric approach and driven by the regression context. The resulting quantile regression estimator has the valuable property of being automatically monotonic across quantile levels. Additionally, the copula-based approach allows the analyst to spontaneously take account of common regression concerns such as interactions between covariates or possible transformations of the latter. From a theoretical prospect, asymptotic normality for both complete and censored data is obtained under classical regularity conditions. Finally, numerical examples as well as a real data application are used to illustrate the validity and finite sample performance of the proposed procedure.

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Electron. J. Statist., Volume 11, Number 1 (2017), 1660-1698.

Received: April 2016
First available in Project Euclid: 25 April 2017

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Semiparametric regression censored quantile regression multidimensional copula modelling semiparametric vine copulas kernel smoothing polynomial local-likelihood probit transformation

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De Backer, Mickaël; El Ghouch, Anouar; Van Keilegom, Ingrid. Semiparametric copula quantile regression for complete or censored data. Electron. J. Statist. 11 (2017), no. 1, 1660--1698. doi:10.1214/17-EJS1273. https://projecteuclid.org/euclid.ejs/1493107294

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