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April 2006 Product-limit estimators of the survival function with twice censored data
Valentin Patilea, Jean-Marie Rolin
Ann. Statist. 34(2): 925-938 (April 2006). DOI: 10.1214/009053606000000065


A model for competing (resp. complementary) risks survival data where the failure time can be left (resp. right) censored is proposed. Product-limit estimators for the survival functions of the individual risks are derived. We deduce the strong convergence of our estimators on the whole real half-line without any additional assumptions and their asymptotic normality under conditions concerning only the observed distribution. When the observations are generated according to the double censoring model introduced by Turnbull, the product-limit estimators represent upper and lower bounds for Turnbull’s estimator.


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Valentin Patilea. Jean-Marie Rolin. "Product-limit estimators of the survival function with twice censored data." Ann. Statist. 34 (2) 925 - 938, April 2006.


Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1092.62099
MathSciNet: MR2283398
Digital Object Identifier: 10.1214/009053606000000065

Primary: 62N01
Secondary: 62G05 , 62N02

Keywords: competing and complementary risks , delta-method , hazard functions , product-limit estimator , strong convergence , Twice censoring , weak convergence

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 2 • April 2006
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