Open Access
Translator Disclaimer
March, 1985 A Combinatoric Approach to the Kaplan-Meier Estimator
David Mauro
Ann. Statist. 13(1): 142-149 (March, 1985). DOI: 10.1214/aos/1176346582

Abstract

The paper considers the Kaplan-Meier estimator $F^{\mathrm{KM}}_n$ from a combinatoric viewpoint. Under the assumption that the estimated distribution $F$ and the censoring distribution $G$ are continuous, the combinatoric results are used to show that $\int |\theta(z)| dF^{\mathrm{KM}}_n(z)$ has expectation not larger than $\int |\theta(z)| dF(z)$ for any sample size $n$. This result is then coupled with Chebychev's inequality to demonstrate the weak convergence of the former integral to the latter if the latter is finite, if $F$ and $G$ are strictly less than 1 on $\mathscr{R}$ and if $\theta$ is continuous.

Citation

Download Citation

David Mauro. "A Combinatoric Approach to the Kaplan-Meier Estimator." Ann. Statist. 13 (1) 142 - 149, March, 1985. https://doi.org/10.1214/aos/1176346582

Information

Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0575.62043
MathSciNet: MR773158
Digital Object Identifier: 10.1214/aos/1176346582

Subjects:
Primary: 60C05
Secondary: 62G05, 62G30, 62G99

Rights: Copyright © 1985 Institute of Mathematical Statistics

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.13 • No. 1 • March, 1985
Back to Top