The Annals of Statistics

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

P. Major and L. Rejto

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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.


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