The Annals of Statistics

Current status data with competing risks: Limiting distribution of the MLE

Piet Groeneboom, Marloes H. Maathuis, and Jon A. Wellner

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Abstract

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.

Article information

Source
Ann. Statist. Volume 36, Number 3 (2008), 1064-1089.

Dates
First available in Project Euclid: 26 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1211819556

Digital Object Identifier
doi:10.1214/009053607000000983

Mathematical Reviews number (MathSciNet)
MR2418649

Zentralblatt MATH identifier
1216.62047

Subjects
Primary: 62N01: Censored data models 62G20: Asymptotic properties
Secondary: 62G05: Estimation

Keywords
Survival analysis current status data competing risks maximum likelihood limiting distribution

Citation

Groeneboom, Piet; Maathuis, Marloes H.; Wellner, Jon A. Current status data with competing risks: Limiting distribution of the MLE. Ann. Statist. 36 (2008), no. 3, 1064--1089. doi:10.1214/009053607000000983. https://projecteuclid.org/euclid.aos/1211819556.


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