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

Global Rates of Convergence of the MLE for Multivariate Interval Censoring