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  Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

Bousquet, O. (2003). Concentration Inequalities for Sub-Additive Functions Using the Entropy Method. In E. Giné, C. Houdré, & D. Nualart (Eds.), Stochastic Inequalities and Applications (pp. 213-247). Basel, Switzerland: Birkhäuser.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-DABF-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0005-7449-7
Genre: Book Chapter

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 Creators:
Bousquet, O1, 2, Author              
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: We obtain exponential concentration inequalities for sub-additive functions of independent random variables under weak conditions on the increments of those functions, like the existence of exponential moments for these increments. As a consequence of these general inequalities, we obtain refinements of Talagrand's inequality for empirical processes and new bounds for randomized empirical processes. These results are obtained by further developing the entropy method introduced by Ledoux.

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 Dates: 2003-11
 Publication Status: Published in print
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 Rev. Method: -
 Identifiers: BibTex Citekey: 2079
DOI: 10.1007/978-3-0348-8069-5_14
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Title: Stochastic Inequalities and Applications
Source Genre: Book
 Creator(s):
Giné, E, Editor
Houdré, C, Editor
Nualart, D, Editor
Affiliations:
-
Publ. Info: Basel, Switzerland : Birkhäuser
Pages: - Volume / Issue: 56 Sequence Number: - Start / End Page: 213 - 247 Identifier: ISBN: 978-3-0348-9428-9

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Title: Progress in Probability
Source Genre: Series
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Pages: - Volume / Issue: 56 Sequence Number: - Start / End Page: - Identifier: -