Semiparametric Copula Quantile Regression for Complete or Censored Data

TL;DR

This paper introduces a flexible semiparametric copula-based method for estimating conditional quantiles in multivariate data, including censored data, ensuring monotonicity and asymptotic normality, with demonstrated effectiveness through simulations and real data.

Contribution

It develops a novel semiparametric copula-based estimator for conditional quantiles applicable to complete and censored data, extending previous methods with improved estimation schemes.

Findings

Estimator is automatically monotonic across quantiles.

Asymptotic normality established under regularity conditions.

Numerical and real data examples demonstrate good finite sample performance.

Abstract

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 complete or right-censored data. In spirit, the methodology is extending the recent work of Noh et al. (2013) and Noh et al. (2015), 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, and 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.