The paper investigates the structure of the self-consistent estimators (SCE) and the nonparametric maximum likelihood estimator (NPMLE) for doubly censored data. An explicit sufficient and necessary condition for an SCE to be the NPMLE is given. Based on this, algorithms for computing the SCE and the NPMLE are provided. The relation between our algorithms and the EM algorithm is studied.
"Algorithms for computing self-consistent and maximum likelihood estimators with doubly censored data." Ann. Statist. 24 (4) 1740 - 1764, August 1996. https://doi.org/10.1214/aos/1032298293