Current status data with competing risks: Consistency and rates of convergence of the MLE
Piet Groeneboom, Marloes H. Maathuis, and Jon A. Wellner
Source: Ann. Statist. Volume 36, Number 3
(2008), 1031-1063.
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.
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Keywords: Survival analysis; current status data; competing risks; maximum likelihood; consistency; rate of convergence
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1211819555
Digital Object Identifier: doi:10.1214/009053607000000974
Mathematical Reviews number (MathSciNet): MR2418648
Zentralblatt MATH identifier: 05294964
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Digital Object Identifier: doi:10.1214/009053607000000983
Project Euclid: euclid.aos/1211819556
Zentralblatt MATH: 05294965
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