Current status data with competing risks: Consistency and rates of Convergence of the MLE

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dc.creatorGroeneboom, Piet
dc.creatorMaathuis, Marloes H.
dc.creatorWellner, Jon A.
dc.date2006-09-01
dc.date2008-06-17
dc.date.accessioned2026-07-07T09:45:40Z
dc.date.available2026-07-07T09:45:40Z
dc.descriptionWe 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 $n^{1/3}$. 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000974 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0609020
dc.identifierhttp://arxiv.org/abs/math/0609020
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 3, 1031-1063
dc.identifierdoi:10.1214/009053607000000974
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163271
dc.subjectStatistics Theory
dc.subject62N01, 62G20 (Primary) 62G05 (Secondary)
dc.titleCurrent status data with competing risks: Consistency and rates of Convergence of the MLE
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