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A Bennett Concentration Inequality and Its Application to Suprema of Empirical Processes

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons83824

Bousquet,  O
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Bousquet, O. (2002). A Bennett Concentration Inequality and Its Application to Suprema of Empirical Processes. C. R. Acad. Sci. Paris, Ser. I, 334, 495-500.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-E084-E
Abstract
We introduce new concentration inequalities for functions on product spaces. They allow to obtain a Bennett type deviation bound for suprema of empirical processes indexed by upper bounded functions. The result is an improvement on Rio's version \citeRio01b} of Talagrand's inequality \cite{Talagrand96 for equidistributed variables.