A semiparametric copula-based estimation of the regression function for right-censored data

This paper addresses the semiparametric estimation of the regression function in a situation where the response variable is right-censored and the covariate(s) is completely observed. We present a new copula-based method to estimate the regression function. The key concept presented in this manuscript is to write the regression function in terms of the copula density and marginal distributions. We suppose a parametric model for the copula density with unknown parameter(s), and we estimate the marginal distributions of the response and the covariate(s) by the Kaplan–Meier estimator and the empirical distribution, respectively. We establish the asymptotic properties of our estimator and extend it to the multivariate case. The proposed method is then applied to analyse a data-set on lifetime with lung-cancer.