Contributions to the theory of product-limit estimators.

Abstract

The product-limit estimator is shown to be a strongly uniformly consistent estimator of the distribution function of a renewal process which started long before the commencement of observation. This product-limit estimator is based on the censored data obtained from independent realizations of such a process in one of two scenarios: one observation per renewal process, and multiple observations per renewal process. In the former scenario a lower bound on the rate of convergence is obtained.