= Empirical likelihood with mixed censoring
For independent event times with <survivor function> $S(t)=\mathbb P(T>t)$, an exact event at $t$ contributes mass $S(t-)-S(t)$, a right-censored observation at $c$ contributes $S(c)$, and an interval-censored observation $l<T\leq u$ contributes $S(l)-S(u)$. Multiplying these factors gives the event-time likelihood when the observation mechanism is noninformative. Maximizing over nonincreasing right-continuous survivor functions gives a <nonparametric maximum-likelihood estimator> rather than requiring a parametric density.
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