Global Rates of Convergence of the MLE for Multivariate Interval Censoring

TL;DR

This paper derives the global convergence rates of the MLE for multivariate interval censored data, showing it converges at a rate of approximately n^{-1/3} with a logarithmic factor depending on dimension.

Contribution

It establishes the first known global convergence rates for the MLE in multivariate interval censored settings, extending previous univariate results.

Findings

Convergence rate is at most n^{-1/3} with a dimension-dependent logarithmic factor.

The rate applies in the Hellinger metric for the multivariate MLE.

Provides theoretical guarantees for the efficiency of the MLE in complex censored data scenarios.

Abstract

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