Current Status Data with Competing Risks: Consistency and Rates of Convergence of the Mle by Piet Groeneboom,
نویسندگان
چکیده
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.
منابع مشابه
Current Status Data with Competing Risks: Limiting Distribution of the Mle.
We study nonparametric estimation 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'. Groeneboom, Maathuis and Wellner [8] proved that both types of estimators converge globally and locally at rate n(1/3). We use these results to derive the local limiting dist...
متن کاملCurrent Status Data with Competing Risks: Consistency and Rates of Convergence of the Mle
Delft University of Technology and Vrije Universiteit Amsterdam, University of Washington and University of Washington 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 the ‘naive estimator’ of Jewell, Van der Laan and ...
متن کاملCurrent Status Data with Competing Risks: Limiting Distribution of the Mle by Piet Groeneboom,
We study nonparametric estimation 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.” Groeneboom, Maathuis and Wellner [Ann. Statist. (2008) 36 1031– 1063] proved that both types of estimators converge globally and locally at rate n1/3. We use these results to...
متن کاملar X iv : m at h / 06 09 02 1 v 1 [ m at h . ST ] 1 S ep 2 00 6 CURRENT STATUS DATA WITH COMPETING RISKS : LIMITING DISTRIBUTION OF THE MLE
Delft University of Technology and Vrije Universiteit Amsterdam, University of Washington and University of Washington We study nonparametric estimation for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider the ‘naive estimator’ of Jewell, Van der Laan and Henneman [10]. Groeneboom, Maathui...
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