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

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 n1/2-consistency, and develop a general methodology for bivariate lifetime modeling, a critical issue in studying reversion conditions that are commonplace in defined benefit pensions and private annuity contracts. An application to goodness-of-fit for survival copula models is discussed. We show that the procedures that we use are consistent, and propose a bootstrap procedure based on our estimator to compute the critical values. The new technique that we propose is tested on the Canadian dataset initially studied by Frees et al. (1996).

► We propose a new estimator of the distribution of two lifetimes. ► These lifetimes are subject to censoring and truncation. ► We derive theoretical convergence results. ► We discuss its implementation. ► We use it to perform goodness-of-fit of copula models on a real dataset.