Current status data with competing risks: Limiting distribution 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: 10.1214/009053607000000983
• 发表日期: 2008
• 页码: 1064-1089
• 关键词: maximum-likelihood-estimation; brownian-motion

摘要

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 10311063] proved that both types of estimators converge globally and locally at rate n(1/3). We use these results to derive the local limiting distributions of the estimators. The limiting distribution of the naive estimator is given by the slopes of the convex minorants of correlated Brownian motion processes with parabolic drifts. The limiting distribution of the MLE involves a new self-induced limiting process. Finally, we present a simulation study showing that the MLE is superior to the naive estimator in terms of mean squared error, both for small sample sizes and asymptotically.