The Annals of Probability

The Oscillation Behavior of Empirical Processes

Winfried Stute

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Abstract

In this paper we study the local behavior of empirical processes for independent identically distributed random variables on the real line. The results are applied to get best rates of convergence for various types of density estimators as well as error estimates for the Bahadur representation of the quantile process obtained by Kiefer.

Article information

Source
Ann. Probab., Volume 10, Number 1 (1982), 86-107.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993915

Digital Object Identifier
doi:10.1214/aop/1176993915

Mathematical Reviews number (MathSciNet)
MR637378

Zentralblatt MATH identifier
0489.60038

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60G17: Sample path properties 62G05: Estimation

Keywords
Empirical process oscillation modulus quantile process Bahadur representation naive density estimator histograms

Citation

Stute, Winfried. The Oscillation Behavior of Empirical Processes. Ann. Probab. 10 (1982), no. 1, 86--107. doi:10.1214/aop/1176993915. https://projecteuclid.org/euclid.aop/1176993915


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