Global rates of convergence of the MLE for multivariate interval censoring

Fuchang Gao; Jon A Wellner

doi:10.1214/13-EJS777

Global rates of convergence of the MLE for multivariate interval censoring

Electron J Stat. 2013:7:364-380. doi: 10.1214/13-EJS777.

Authors

Fuchang Gao¹, Jon A Wellner

Affiliation

¹ Department of Mathematics, University of Idaho, Moscow, Idaho 83844-1103, fuchang@uidaho.edu.

Abstract

We establish global rates of convergence of the Maximum Likelihood Estimator (MLE) of a multivariate distribution function on 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)^γ for γ = (5d - 4)/6.

Keywords: Empirical processes; Hellinger metric; global rate; interval censoring; multivariate; multivariate monotone functions.

Abstract

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