Concentration inequalities for separately convex functions

Abstract : We provide new comparison inequalities for separately convex functions of independent random variables. Our method is based on the decomposition in Doob martingale. However we only impose that the martingale increments are stochastically bounded. For this purpose, building on the results of Bentkus ([4], [5], [6]), we establish comparison inequalities for random variables stochastically dominated from below and from above. We illustrate our main results by showing how they can be used to derive deviation or moment inequalities for functions which are both separately convex and separately Lipschitz, weighted empirical distribution functions, suprema of randomized empirical processes and chaos of order two.
Type de document :
Pré-publication, Document de travail
2016
Liste complète des métadonnées

Littérature citée [26 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01344861
Contributeur : Antoine Marchina <>
Soumis le : mardi 12 juillet 2016 - 16:58:16
Dernière modification le : jeudi 11 janvier 2018 - 02:02:45

Fichier

article_1.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01344861, version 1

Citation

Antoine Marchina. Concentration inequalities for separately convex functions. 2016. 〈hal-01344861〉

Partager

Métriques

Consultations de la notice

319

Téléchargements de fichiers

117