## The Annals of Statistics

- Ann. Statist.
- Volume 16, Number 3 (1988), 1113-1132.

### Strong Embedding of the Estimator of the Distribution Function under Random Censorship

#### Abstract

In this paper the asymptotic behaviour of the product limit estimator $F_n$ of an unknown distribution is investigated. We give an approximation of the difference $F_n(x) - F(x)$ by a Gaussian process and also by the average of i.i.d. processes. We get almost as good an approximation of the stochastic process $F_n(x) - F(x)$ as one can get for the analogous problem when the maximum likelihood estimator is approximated by a Gaussian random variable or by the average of i.i.d. random variables in the parametric case.

#### Article information

**Source**

Ann. Statist. Volume 16, Number 3 (1988), 1113-1132.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176350949

**Digital Object Identifier**

doi:10.1214/aos/1176350949

**Mathematical Reviews number (MathSciNet)**

MR959190

**Zentralblatt MATH identifier**

0667.62024

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60F15: Strong theorems

Secondary: 60F17: Functional limit theorems; invariance principles 62G05: Estimation

**Keywords**

Censored sample product limit estimator

#### Citation

Major, P.; Rejto, L. Strong Embedding of the Estimator of the Distribution Function under Random Censorship. Ann. Statist. 16 (1988), no. 3, 1113--1132. doi:10.1214/aos/1176350949. http://projecteuclid.org/euclid.aos/1176350949.