## The Annals of Statistics

### Estimating a Distribution Function

Rudolf Beran

#### Abstract

It is shown that the limiting distribution of any regular estimator of a continuous cdf on [0, 1] can be represented as a convolution of the Brownian bridge process with another distribution on $C\lbrack 0, 1\rbrack$. The result is related to Hajek's representation for limiting distributions of regular parametric estimators.

#### Article information

Source
Ann. Statist. Volume 5, Number 2 (1977), 400-404.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176343806

JSTOR

Digital Object Identifier
doi:10.1214/aos/1176343806

Mathematical Reviews number (MathSciNet)
MR445701

Zentralblatt MATH identifier
0379.62024

Subjects
Primary: 62G05: Estimation
Secondary: 62E20: Asymptotic distribution theory

#### Citation

Beran, Rudolf. Estimating a Distribution Function. The Annals of Statistics 5 (1977), no. 2, 400--404. doi:10.1214/aos/1176343806. http://projecteuclid.org/euclid.aos/1176343806.