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March, 1992 Some Inequalities About the Kaplan-Meier Estimator
Song Yang
Ann. Statist. 20(1): 535-544 (March, 1992). DOI: 10.1214/aos/1176348537


In this paper we consider the product-limit estimator of the survival distribution function in the context of independent but nonidentically distributed censoring times. An upper bound on the mean square increment of the stopped Kaplan-Meier process is obtained. Also, a representation is given for the ratio of the survival distribution function to the product-limit estimator as the product of a bounded process and a martingale. From this representation bounds on the mean square of the ratio and on the tail probability of the sup norm of the ratio are derived.


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Song Yang. "Some Inequalities About the Kaplan-Meier Estimator." Ann. Statist. 20 (1) 535 - 544, March, 1992.


Published: March, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62037
MathSciNet: MR1150359
Digital Object Identifier: 10.1214/aos/1176348537

Primary: 62E20
Secondary: 62G99 , 62M99

Keywords: Gronwall's inequality , martingale , product-limit estimator , Volterra integral equation

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • March, 1992
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