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Inégalités de concentration pour les processus empiriques de classes de parties
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  • Published: February 2001

Inégalités de concentration pour les processus empiriques de classes de parties

Concentration inequalities for set-indexed empirical processes

  • Emmanuel Rio1 

Probability Theory and Related Fields volume 119, pages 163–175 (2001)Cite this article

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Abstract.

We propose new concentration inequalities for maxima of set-indexed empirical processes. Our approach is based either on entropy inequalities or on martingale methods. The improvements we get concern the rate function which is exactly the large deviations rate function of a binomial law in most of the cases.

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Authors and Affiliations

  1. EP 1755 CNRS, Université de Versailles, Saint-Quentin en Yvelines, Bâtiment Fermat, 45, avenue des États-Unis, 78035 Versailles Cedex, France. e-mail: Emmanuel.Rio@math.uvsq.fr, , , , , , FR

    Emmanuel Rio

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  1. Emmanuel Rio
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Received: 11 January 2000 / Revised version: 12 May 2000 / Published online: 14 December 2000

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Rio, E. Inégalités de concentration pour les processus empiriques de classes de parties . Probab Theory Relat Fields 119, 163–175 (2001). https://doi.org/10.1007/PL00008756

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  • Issue Date: February 2001

  • DOI: https://doi.org/10.1007/PL00008756

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  • Mathematics Subject Classification (2000): 60 E 15, 60 F 10
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