A model of interval censorship of a failure time T is considered when there is only one inspection time Y. The observable data are n independent copies of the pair $(Y, \delta)$, where $\delta = [T \leq Y]$. We construct a class of self-consistent estimators of the survival function of T defined implicitly through two equations and show their strong consistency under certain conditions. The properties of the onparametric maximum likelihood estimator are also investigated.
"A class of estimators of the survival function from interval-censored data." Ann. Statist. 24 (2) 647 - 658, April 1996. https://doi.org/10.1214/aos/1032894457