Global Rates of Convergence of the MLE for Multivariate Interval   Censoring
  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 of the MLE in the Hellinger metric is no worse than $n^{-1/3} (\log n)^{\gamma}$ for $\gamma = (5d - 4)/6$. 
Jon A. Wellner and Fuchang Gao
math.ST stat.TH