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.
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.
Accepted:
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Antoine Marchina 1, 2
@article{CRMATH_2019__357_6_537_0, author = {Antoine Marchina}, 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}, }
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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