## The Annals of Statistics

### 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

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