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June 2008 Current status data with competing risks: Limiting distribution of the MLE
Piet Groeneboom, Marloes H. Maathuis, Jon A. Wellner
Ann. Statist. 36(3): 1064-1089 (June 2008). DOI: 10.1214/009053607000000983


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 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.


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Piet Groeneboom. Marloes H. Maathuis. Jon A. Wellner. "Current status data with competing risks: Limiting distribution of the MLE." Ann. Statist. 36 (3) 1064 - 1089, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1216.62047
MathSciNet: MR2418649
Digital Object Identifier: 10.1214/009053607000000983

Primary: 62G20 , 62N01
Secondary: 62G05

Keywords: competing risks , Current status data , Limiting distribution , maximum likelihood , Survival analysis

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 3 • June 2008
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