Empirical Bayes Estimation of a Distribution (Survival) Function from Right Censored Observations

Abstract

This paper provides an empirical Bayes approach to the problem of nonparametric estimation of a distribution (or survival) function when the observations are censored on the right. The results use the notion of a Dirichlet process prior introduced by Ferguson. The paper presents a generalization to the case of right censored observations of the rate result of an empirical Bayes nonparametric estimator of a distribution function of Korwar and Hollander in the uncensored case. The rate of asymptotic convergence of optimality is shown to be the best obtainable for the problem considered.