Nonparametric estimation of the copula function with bivariate twice censored data

Abstract

In this work, we are interested in the nonparametric estimation of the copula function in the presence of bivariate twice censored data. Assuming that the copula functions of the right and the left censoring variables are known, we propose an estimator of the joint distribution function of the variables of interest, then we derive an estimator of their copula function. Using a representation of the proposed estimator of the joint distribution function as a sum of independent and identically distributed variables, we establish the weak convergence of the empirical copula that we introduce.