Asymptotic normality of the truncation probability estimator for truncated dependent data

Abstract

In some long term studies, a series of dependent and possibly truncated life-times may be observed. Suppose that the lifetimes have a common marginal distribution function. In left-truncation model, one observes data (Xi,Ti) only, when Ti ≤ Xi. Under some regularity conditions, we provide a strong representation of the sn estimator of s = P(Ti ≤ Xi), in the form of an average of random variables plus a remainder term. This representation en-ables us to obtain the asymptotic normality for sn .