Panchenko, Dmitriy Some extensions of an inequality of Vapnik and Chervonenkis. (English) Zbl 1008.60035 Electron. Commun. Probab. 7, Paper No. 6, 55-65 (2002). Summary: 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. Cited in 5 Documents MSC: 60E15 Inequalities; stochastic orderings 28A35 Measures and integrals in product spaces Keywords:concentration of measure; empirical processes PDFBibTeX XMLCite \textit{D. Panchenko}, Electron. Commun. Probab. 7, Paper No. 6, 55--65 (2002; Zbl 1008.60035) Full Text: DOI arXiv EuDML EMIS