The Annals of Statistics

A Combinatoric Approach to the Kaplan-Meier Estimator

David Mauro

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 142-149.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346582

Digital Object Identifier
doi:10.1214/aos/1176346582

Mathematical Reviews number (MathSciNet)
MR773158

Zentralblatt MATH identifier
0575.62043

JSTOR
links.jstor.org

Subjects
Primary: 60C05: Combinatorial probability
Secondary: 62G05: Estimation 62G30: Order statistics; empirical distribution functions 62G99: None of the above, but in this section

Keywords
Censored Kaplan-Meier estimator

Citation

Mauro, David. A Combinatoric Approach to the Kaplan-Meier Estimator. Ann. Statist. 13 (1985), no. 1, 142--149. doi:10.1214/aos/1176346582. https://projecteuclid.org/euclid.aos/1176346582


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