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.
Citation
Dmitriy Panchenko. "Some Extensions of an Inequality of Vapnik and Chervonenkis." Electron. Commun. Probab. 7 55 - 65, 2002. https://doi.org/10.1214/ECP.v7-1047
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