Estimators for Survival Function when Censoring Times are Known

Abstract

Under the random censorship model with extra assumption that all censoring times are known, Chiu (1999) proposed a new estimator for the survival function of failure time. In this article, we explore the most likely uniformly consistent estimators of the survival function in such data settings and study large sample properties of these estimators. It turns out that the classical Kaplan-Meier estimator is of the smallest asymptotic variance among these possible estimators. This fact confirms the optimality of the Kaplan-Meier estimator in term of asymptotic variance and may suggest that the Kaplan-Meier estimator is the most recommendable even in such circumstances.

Key Words:

• Asymptotic variance
• Kaplan-Meier estimator
• Martingale
• Survival analysis