## The Annals of Statistics

### A Combinatoric Approach to the Kaplan-Meier Estimator

David Mauro

#### 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

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