Asymptotic Variance of the Gmle of a Survival Function with Interval-censored Data

Interval-censored data are generated by a random survival time X and a random censoring interval. We either observe the exact survival time or only know the survival time lies within the censoring interval. Turnbull (1976) proposes a self-consistent algorithm for obtaining the generalized maximum likelihood estimator (GMLE) of a survival function with interval-censored data. Yu, Li and Wong (1996) prove the strong consistency of the GMLE. In this paper, we establish the asymptotic normality of the GMLE and self-consistent estimators (SCE) and present a consistent estimator of the asymptotic variance of the GMLE and SCEs with interval-censored data.