Current status data with competing risks: Consistency and rates of convergence of the MLE
成果类型：
Article
署名作者：
Groeneboom, Piet; Maathuis, Marloes H.; Wellner, Jon A.
署名单位：
Delft University of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Washington; University of Washington Seattle; Vrije Universiteit Amsterdam
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/009053607000000974
发表日期：
2008
页码：
1031-1063
关键词：
摘要：
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 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.