Global Rates of Convergence of the MLE for Multivariate Interval Censoring

Jon A. Wellner, Fuchang Gao

Published 2012-10-02, updated 2012-12-27Version 2

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 $\gamma = (5d - 4)/6$.