The Annals of Statistics

Some Inequalities About the Kaplan-Meier Estimator

Song Yang

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Abstract

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.

Article information

Source
Ann. Statist., Volume 20, Number 1 (1992), 535-544.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348537

Digital Object Identifier
doi:10.1214/aos/1176348537

Mathematical Reviews number (MathSciNet)
MR1150359

Zentralblatt MATH identifier
0745.62037

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G99: None of the above, but in this section 62M99: None of the above, but in this section

Keywords
Product-limit estimator martingale Volterra integral equation Gronwall's inequality

Citation

Yang, Song. Some Inequalities About the Kaplan-Meier Estimator. Ann. Statist. 20 (1992), no. 1, 535--544. doi:10.1214/aos/1176348537. https://projecteuclid.org/euclid.aos/1176348537


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