Nonparametric Estimation of a distribution function from doubly truncated data under dependence

The NPMLE of a distribution function from doubly truncated data was introduced in the seminal paper of Efron and Petrosian. The consistency of the Efron-Petrosian estimator depends however on the assumption of independent truncation. In this work we introduce an extension of the Efron-Petrosian NPMLE when the variable of interest and the truncation variables may be dependent. The proposed estimator is constructed on the basis of a copula function which represents the dependence structure between the variable of interest and the truncation variables. Two different iterative algorithms to compute the estimator in practice are introduced, and their performance is explored through an intensive Monte Carlo simulation study. We illustrate the use of the estimators on two real data examples.