Dmitry Panchenko
Published 2004-05-18Version 1
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.
Comments: 12 pages
Journal: 2002 Elect. Comm. in Probab. 7 55-65
Poincaré inequality for non euclidean metrics and transportation cost inequalities on $\mathbb{R}^d$
Real roots of random polynomials: expectation and repulsion
An Inequality Related to Negative Definite Functions
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