[Une inégalité exponentielle pour les suprema de processus empiriques avec queues lourdes sur la gauche]
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.
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@article{CRMATH_2019__357_6_537_0,
author = {Marchina, Antoine},
title = {An exponential inequality for suprema of empirical processes with heavy tails on the left},
journal = {Comptes Rendus. Math\'ematique},
pages = {537--544},
publisher = {Elsevier},
volume = {357},
number = {6},
year = {2019},
doi = {10.1016/j.crma.2019.06.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.06.008/}
}
TY - JOUR AU - Marchina, Antoine TI - An exponential inequality for suprema of empirical processes with heavy tails on the left JO - Comptes Rendus. Mathématique PY - 2019 SP - 537 EP - 544 VL - 357 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.06.008/ DO - 10.1016/j.crma.2019.06.008 LA - en ID - CRMATH_2019__357_6_537_0 ER -
%0 Journal Article %A Marchina, Antoine %T An exponential inequality for suprema of empirical processes with heavy tails on the left %J Comptes Rendus. Mathématique %D 2019 %P 537-544 %V 357 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.06.008/ %R 10.1016/j.crma.2019.06.008 %G en %F CRMATH_2019__357_6_537_0
Marchina, Antoine. An exponential inequality for suprema of empirical processes with heavy tails on the left. Comptes Rendus. Mathématique, Tome 357 (2019) no. 6, pp. 537-544. doi : 10.1016/j.crma.2019.06.008. http://www.numdam.org/articles/10.1016/j.crma.2019.06.008/
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