Institute of Mathematical Statistics Lecture Notes - Monograph Series

Modified empirical CLT’s under only pre-Gaussian conditions

Shahar Mendelson and Joel Zinn

Full-text: Open access

Abstract

We show that a modified Empirical process converges to the limiting Gaussian process whenever the limit is continuous. The modification depends on the properties of the limit via Talagrand's characterization of the continuity of Gaussian processes.

Chapter information

Source
Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn, eds., High Dimensional Probability: Proceedings of the Fourth International Conference (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 173-184

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196284111

Digital Object Identifier
doi:10.1214/074921706000000833

Mathematical Reviews number (MathSciNet)
MR2387768

Zentralblatt MATH identifier
1122.60028

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles

Keywords
central limit theorems empirical processes

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Mendelson, Shahar; Zinn, Joel. Modified empirical CLT’s under only pre-Gaussian conditions. High Dimensional Probability, 173--184, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000833. https://projecteuclid.org/euclid.lnms/1196284111


Export citation