Survival function and density estimation for truncated dependent data

In some long-term studies, a series of dependent and possibly truncated lifetimes may be observed. Suppose that the lifetimes have a common marginal distribution function. Under some regularity conditions, we provide a strong representation of the product-limit estimator in the form of an average of random variables plus a remainder term. In addition, we also give asymptotic representations for the kernel estimators of the density and the hazard rate. These representations enable us to obtain the asymptotic normality and the uniform consistency of the estimators.