Comptes Rendus
no. 6
Probability theory/Statistics
An exponential inequality for suprema of empirical processes with heavy tails on the left
[Une inégalité exponentielle pour les suprema de processus empiriques avec queues lourdes sur la gauche]

Présenté par : Michel Talagrand

Antoine Marchina1, 2
1 Université Paris-Est, LAMA (UMR 8050), UPEM, UPEC, CNRS, 77454 Marne-la-Vallée, France
2 Laboratoire de mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035 Versailles, France
Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 537-544.

Dans cette Note, nous donnons des inégalités exponentielles pour les suprema de processus empiriques avec queues lourdes sur la gauche. Notre approche est basée sur une décomposition en martingale, associée à des inégalités de comparaison sur un cône de fonctions convexes, initialement introduit par Pinelis. Les constantes données sont explicites.

In this Note, we provide exponential inequalities for suprema of empirical processes with heavy tails on the left. Our approach is based on a martingale decomposition, associated with comparison inequalities over a cone of convex functions originally introduced by Pinelis. Furthermore, the constants in our inequalities are explicit.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.06.008
Antoine Marchina 1, 2

1 Université Paris-Est, LAMA (UMR 8050), UPEM, UPEC, CNRS, 77454 Marne-la-Vallée, France
2 Laboratoire de mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay, 78035 Versailles, France 
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Antoine Marchina. An exponential inequality for suprema of empirical processes with heavy tails on the left. Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 537-544. doi : 10.1016/j.crma.2019.06.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.06.008/

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