Asymptotic normality of the truncation probability estimator for truncated dependent data

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 (Xj,Tj) only, when Tʹi < X{. Under some regularity conditions, we provide a strong representation of the j3n estimator of /? = /ʹ( /, < 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 j3n.