### Estimating a Distribution Function

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

#### 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.

First Page:
Primary Subjects: 62G05
Secondary Subjects: 62E20
Full-text: Open access