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

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dc.creatorGroeneboom, Piet
dc.creatorMaathuis, Marloes H.
dc.creatorWellner, Jon A.
dc.date2006-09-01
dc.date2008-06-17
dc.date.accessioned2026-07-07T09:45:40Z
dc.date.available2026-07-07T09:45:40Z
dc.descriptionWe 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 $n^{1/3}$. 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000983 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0609021
dc.identifierhttp://arxiv.org/abs/math/0609021
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 3, 1064-1089
dc.identifierdoi:10.1214/009053607000000983
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163272
dc.subjectStatistics Theory
dc.subject62N01, 62G20 (Primary) 62G05 (Secondary)
dc.titleCurrent status data with competing risks: Limiting distribution of the MLE
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