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October 2003 Symmetrization approach to concentration inequalities for empirical processes
Dmitry Panchenko
Ann. Probab. 31(4): 2068-2081 (October 2003). DOI: 10.1214/aop/1068646378


We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of controlling the deviation between two independent copies of the functional. As an application we give a new easy proof of Talagrand's concentration inequality for empirical processes, where besides symmetrization we use only Talagrand's concentration inequality on the discrete cube $\{0,1\}^n.$ As another application of this technique we prove new Vapnik--Chervonenkis type inequalities. For example, for VC-classes of functions we prove a classical inequality of Vapnik and Chervonenkis only with normalization by the sum of variance and sample variance.


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Dmitry Panchenko. "Symmetrization approach to concentration inequalities for empirical processes." Ann. Probab. 31 (4) 2068 - 2081, October 2003.


Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1042.60008
MathSciNet: MR2016612
Digital Object Identifier: 10.1214/aop/1068646378

Primary: 60E15
Secondary: 60F10

Keywords: Concentration inequalities , Empirical processes

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • October 2003
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