## The Annals of Statistics

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

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

#### 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