Some extensions of an inequality of Vapnik and Chervonenkis

2004/05/18 by Dmitry Panchenko
Mathematics · #math.PR #msc:60G20

paper · pdf

published as 2002 Elect. Comm. in Probab. 7 55-65 · 12 pages

arxiv created 2004/05/18 · arxiv updated 2009/12/01

Abstract

The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample average uniformly over a VC-major class of functions taking into account the size of the expectation. Using Talagrand's kernel method we prove a similar result for the classes of functions for which Dudley's uniform entropy integral or bracketing entropy integral is finite.

Related

• Uniform Approximation of Vapnik-Chervonenkis Classes
• Bounding the expectation of the supremum of an empirical process over a (weak) vc-major class
• Entropy numbers of classes defined by integral operators
• A local maximal inequality under uniform entropy
• A uniform Dvoretzky-Kiefer-Wolfowitz inequality