A generalization of the Kaplan–Meier estimator for analyzing bivariate mortality under right-censoring and left-truncation with applications in model-checking for survival copula models

摘要

In this paper, we provide a new nonparametric estimator of the joint distribution of two lifetimes under random right censoring and left truncation, which can be seen as a bivariate extension of the Kaplan-Meier estimator. We derive asymptotic results for this estimator, including uniform $n^{1/2}-$consistency, and develop a general methodology to study bivariate lifetime modelling, which is a critical issue in the study of pensions with a reversion condition. Application to goodness-of-fit for survival copula models is discussed. We show that the procedure that we use are consistent, and propose a bootstrap procedure based on our estimator to compute the critical values. All the new techniques that we propose are experimented on the Canadian data-set initially studied by Frees et al. (1996).