Abstract: In this paper, we study the Nonparametric Maximum Likelihood Estimator (NPMLE) of univariate ``Mixed Case'' interval-censored data in which the number of observation times, and the observation times themselves are random variables. We provide a characterization of the NPMLE, then use the ICM algorithm to compute the NPMLE. We also study the asymptotic properties of the NPMLE: consistency, global rates of convergence with and without a separation condition, and an asymptotic minimax lower bound.
Key words and phrases: Consistency, convex minorant algorithm, empirical processes, interval censored data, maximum likelihood, rate of convergence.