Concentration inequalities for separately convex functions

Antoine Marchina (1)

1 LMV - Laboratoire de Mathématiques de Versailles

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.

Mots clés: concentration inequalities; deviation inequalities; generalized moments; martingale method; empirical processes; Pinelis' inequality; Bentkus' inequality

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Antoine Marchina. Concentration inequalities for separately convex functions. Bernoulli, 2018, 24 (4A), pp.2906-2933. ⟨10.3150/17-BEJ949⟩. ⟨hal-01344861v2⟩