Semiparametric copula quantile regression for complete or censored data

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) andNoh 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.

Semiparametric quantile regression with random censoring

“…Figure 1 approx. here To measure the performance of the estimators b θ τ ( ) for the nonparametric components, we use the (empirical) integrated mean squared error (IMSE) as in De Backer et al (2017), which is given by…”

Examination and visualisation of the simplifying assumption for vine copulas in three dimensions

“…() presented a sequential estimation method for vine copulas. Vine models were used for quantile regression in Noh, Ghouch & Van Keilegom (), De Backer, Ghouch & Van Keilegom () and Kraus & Czado () and the dependence of finite block maxima of vine copulas was investigated in Killiches & Czado (). To extend the approach to non‐continuous models Panagiotelis, Czado & Joe () as well as Stöber et al .…”

High-Dimensional Spatial Quantile Function-on-Scalar Regression

“…Second, we employ a parametric copula model to directly delineate the spatial dependence of image data within each subject. In contrast, most existing copula models were applied to quantile regression for different purposes and data types (Chen et al, 2009;Bouyé and Salmon, 2013;Kraus and Czado, 2017;De Backer et al, 2017;Wang et al, 2019). For instance, in Wang et al (2019), the copula was used to model the temporal dependence of longitudinal data, while it is assumed a linear quantile regression model with…”