Estimation of a bivariate conditional copula when a variable is subject to random right censoring

Abstract

This paper concerns the dependence structure of a random pair $(Y_{1},Y_{2})$ conditionally upon a covariate $X$ in the case where the variable $Y_{1}$ is subject to random right censoring. The dependence structure is described by a conditional copula for which we propose a nonparametric estimator. We establish the asymptotic properties of the proposed estimator and investigate its finite sample behavior in a numerical study. The methodology is illustrated through a real data example featuring patients with advanced lung cancer.