De Backer, Mickaël
[UCL]
El Ghouch, Anouar
[UCL]
Van Keilegom, Ingrid
[UCL]
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.
| Bibliographic reference |
De Backer, Mickaël ; El Ghouch, Anouar ; Van Keilegom, Ingrid. Semiparametric copula quantile regression for complete or censored data. In: Electronic Journal of Statistics, Vol. 11, no.1, p. 1660-1698 (2017) |
| Permanent URL |
http://hdl.handle.net/2078.1/185666 |
