Comptes Rendus
no. 6
Une inégalité de concentration à gauche pour les processus empiriques
Thierry Klein1
1 Laboratoire de mathématiques, LAMA CNRS UMR 8100, Université de Versailles–Saint-Quentin, Versailles, France
Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 501-504.

Nous donnons des constantes dans l'inégalité de concentration à gauche de Talagrand pour les processus empiriques indexés par des classes de fonctions, en partant de la méthode de Herbst. Le point nouveau est que la constante du facteur variance est exacte, ce qui répond à une conjecture de Massart.

We give new constants in Talagrand's left concentration inequality for maxima of empirical processes. Our approach is based on the Herbst method. The improvement we get concerns the constant in the variance factor, which is the one conjectured by Massart.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02303-8

Thierry Klein 1

1 Laboratoire de mathématiques, LAMA CNRS UMR 8100, Université de Versailles–Saint-Quentin, Versailles, France 
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Thierry Klein. Une inégalité de concentration à gauche pour les processus empiriques. Comptes Rendus. Mathématique, Volume 334 (2002) no. 6, pp. 501-504. doi : 10.1016/S1631-073X(02)02303-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02303-8/

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[4] E. Rio, Une inégalité de Bernstein pour les maxima de processus empiriques, Preprint 57 de l'Université de Versailles–Saint-Quentin, 2001

[5] M. Talagrand New concentration inequalities in product spaces, Invent. Math., Volume 126 (1996), pp. 503-563

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