Self-consistent estimators of survival functions with doubly-censored data

The consistency and asymptotic normality of self-consistent estimators (SCE) of survival functions with doubly-censored data have been studied by many authors. However, to the best of our knowledge, expressions of the asymptotic variance of the SCE have not been derived in the literature. In this paper, under the assumption that the survival time and censoring time distributions are discrete with finitely many jump points, an expression and a consistent estimator of the asymptotic variance of the SCE are presented. A proof of the strong consistency of the SCE is also presented. Our simulation studies indicate that the estimate of the asymptotic variance is very close to the true value even with moderate sample sizes and high censoring rates.