We establish global rates of convergence of the Maximum Likelihood Estimator (MLE) of a multivariate distribution function on Rd 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) γ for γ = (5d − 4)/6. AMS 2000 subject classifications: Primary 62G07, 62H12; secondary 62G05, 62G20.

Keywords and phrases: empirical processes, global rate, Hellinger metric, interval censoring, multivariate, multivariate monotone functions.