Some extensions of an inequality of Vapnik and Chervonenkis

Details Some extensions of an inequality of Vapnik and Chervonenkis Some extensions of an inequality of Vapnik and Chervonenkis

2004-05-18

arxiv.org/abs/math/0405342v1

2002 Elect. Comm. in Probab. 7 55-65

Mathematics

Probability

12 pages

Scientific paper

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.

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