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Global rates of convergence of the MLE for multivariate interval censoring. (English) Zbl 1336.62128
Summary: 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 $$\gamma =(5d-4)/6$$.

##### MSC:
 62H12 Estimation in multivariate analysis 62N01 Censored data models 62G07 Density estimation 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference
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