The Annals of Probability

Empirical Processes Indexed by Lipschitz Functions

Evarist Gine and Joel Zinn

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Abstract

Necessary and sufficient conditions on $P$ for the unit balls of $BL(\mathbf{R})$ and $\operatorname{Lip}(\mathbf{R})$ to be functional $P$-Donsker classes are obtained.

Article information

Source
Ann. Probab., Volume 14, Number 4 (1986), 1329-1338.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176992373

Digital Object Identifier
doi:10.1214/aop/1176992373

Mathematical Reviews number (MathSciNet)
MR866353

Zentralblatt MATH identifier
0611.60029

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles

Keywords
Empirical processes functional Donsker classes Lipschitz and bounded Lipschitz functions

Citation

Gine, Evarist; Zinn, Joel. Empirical Processes Indexed by Lipschitz Functions. Ann. Probab. 14 (1986), no. 4, 1329--1338. doi:10.1214/aop/1176992373. https://projecteuclid.org/euclid.aop/1176992373


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