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June 2008 Current status data with competing risks: Consistency and rates of convergence of the MLE
Piet Groeneboom, Marloes H. Maathuis, Jon A. Wellner
Ann. Statist. 36(3): 1031-1063 (June 2008). DOI: 10.1214/009053607000000974

Abstract

We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler “naive estimator.” Both types of estimators were studied by Jewell, van der Laan and Henneman [Biometrika (2003) 90 183–197], but little was known about their large sample properties. We have started to fill this gap, by proving that the estimators are consistent and converge globally and locally at rate n1/3. We also show that this local rate of convergence is optimal in a minimax sense. The proof of the local rate of convergence of the MLE uses new methods, and relies on a rate result for the sum of the MLEs of the sub-distribution functions which holds uniformly on a fixed neighborhood of a point. Our results are used in Groeneboom, Maathuis and Wellner [Ann. Statist. (2008) 36 1064–1089] to obtain the local limiting distributions of the estimators.

Citation

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Piet Groeneboom. Marloes H. Maathuis. Jon A. Wellner. "Current status data with competing risks: Consistency and rates of convergence of the MLE." Ann. Statist. 36 (3) 1031 - 1063, June 2008. https://doi.org/10.1214/009053607000000974

Information

Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1360.62123
MathSciNet: MR2418648
Digital Object Identifier: 10.1214/009053607000000974

Subjects:
Primary: 62G20, 62N01
Secondary: 62G05

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 3 • June 2008
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