Open Access
August 2002 Random censoring in set-indexed survival analysis
B. Gail Ivanoff, Ely Merzbach
Ann. Appl. Probab. 12(3): 944-971 (August 2002). DOI: 10.1214/aoap/1031863176


Using the theory of set-indexed martingales, we develop a general model for survival analysis with censored data which is parameterized by sets instead of time points. We define a set-indexed Nelson--Aalen estimator for the integrated hazard function with the presence of a censoring by a random set which is a stopping set. We prove that this estimator is asymptotically unbiased and consistent. A central limit theorem is given. This model can be applied to cases when censoring occurs in geometrical objects or patterns, and is a generalization of models with multidimensional failure times.


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B. Gail Ivanoff. Ely Merzbach. "Random censoring in set-indexed survival analysis." Ann. Appl. Probab. 12 (3) 944 - 971, August 2002.


Published: August 2002
First available in Project Euclid: 12 September 2002

zbMATH: 1010.62091
MathSciNet: MR1925447
Digital Object Identifier: 10.1214/aoap/1031863176

Primary: 60G42 , 60G55 , 62G05

Keywords: Censoring , central limit theorem , estimator , hazard function , set-indexed martingale , stopping set , Survival analysis , Volterra equation

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.12 • No. 3 • August 2002
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