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October 1999 Laws of the Iterated Logarithm for Censored Data
Evarist Giné, Armelle Guillou
Ann. Probab. 27(4): 2042-2067 (October 1999). DOI: 10.1214/aop/1022874828


First- and second-order laws of the iterated logarithm are obtained for both the Nelson–Aalen and the Kaplan–Meier estimators in the random censorship model, uniform up to a large order statistic of the censored data. The rates for the first-order processes are exact except for constants. The LIL for the second-order processes (where one subtracts a linear, empirical process, term from the difference between the original process and the estimator), uniform over fixed intervals, is also proved. Somewhat surprisingly, there is a certain degree of proof unification for fixed and variable intervals in the second-order results for the Nelson–Aalen estimator. No assumptions are made on the distribution of the censoring variables and only continuity of the distribution function of the original variables is assumed for the results on the Kaplan–Meier estimator.


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Evarist Giné. Armelle Guillou. "Laws of the Iterated Logarithm for Censored Data." Ann. Probab. 27 (4) 2042 - 2067, October 1999.


Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0984.62023
MathSciNet: MR1742901
Digital Object Identifier: 10.1214/aop/1022874828

Primary: 60F15 , 62G05
Secondary: 62G20 , 62G30

Keywords: cumulative hazard function , Law of the iterated logarithm , product limit estimator , random censorship , U-processes , U-statistics

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • October 1999
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