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A note on bounds for VC dimensions

Jon A. Wellner and Aad van der Vaart

Full-text: Open access

Abstract

We provide bounds for the VC dimension of class of sets formed by unions, intersections, and products of VC classes of sets $\mathcal{C}$1, …, $\mathcal{C}$m.

Chapter information

Source
Christian Houdré, Vladimir Koltchinskii, David M. Mason and Magda Peligrad, eds., High Dimensional Probability V: The Luminy Volume (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 103-107

Dates
First available in Project Euclid: 2 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1265119264

Digital Object Identifier
doi:10.1214/09-IMSCOLL508

Mathematical Reviews number (MathSciNet)
MR2797943

Zentralblatt MATH identifier
1243.60009

Subjects
Primary: 60B99: None of the above, but in this section
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Vapnik-Chervonenkis class combining classes inequality entropy

Rights
Copyright © 2009, Institute of Mathematical Statistics

Citation

van der Vaart, Aad; Wellner, Jon A. A note on bounds for VC dimensions. High Dimensional Probability V: The Luminy Volume, 103--107, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2009. doi:10.1214/09-IMSCOLL508. https://projecteuclid.org/euclid.imsc/1265119264


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