Self-consistent estimators for estimating distribution functions from incomplete data are presented. In many cases these estimators are also generalized maximum likelihood estimators. In this paper we discuss the theoretical properties of such estimators: existence, uniform consistency, law of the iterated logarithm, and weak convergence. Applications to the product limit estimator for right-censored data and to the estimator proposed by Turnbull (1974, 1976) for doubly (right- and left-) censored data are also given.
"A Large Sample Study of Generalized Maximum Likelihood Estimators from Incomplete Data Via Self-Consistency." Ann. Statist. 13 (4) 1317 - 1334, December, 1985. https://doi.org/10.1214/aos/1176349740