Global rates of convergence of the MLE for multivariate interval censoring

Abstract

We establish global rates of convergence of the Maximum Likelihood Estimator (MLE) of a multivariate distribution function on ${\mathbb{R}}^{d}$ in the case of (one type of) “interval censored” data. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than $n^{-1/3}(\log n)^{\gamma}$ for $\gamma =(5d-4)/6$.