A Note on Empirical Bayes Estimation of a Distribution Function Based on Censored Data

Abstract

Susarla and Van Ryzin exhibited an empirical Bayes estimator of a distribution function $F$ based on randomly right-censored observations. In a later paper they obtained a different estimator which alleviates the weaknesses of their earlier estimator and showed that it is asymptotically optimal with rate of convergence $n^{-1}$. The purpose of this note is to present a slightly different estimator which is simpler and is also asymptotically optimal with the same rate of convergence. Their numerical example is reworked to show that the estimator is a proper distribution function.