About the rate function in concentration inequalities for suprema of bounded empirical processes

Antoine Marchina (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We provide new deviation inequalities in the large deviations band-width for suprema of empirical processes indexed by classes of uniformly bounded functions associated with independent and identically distributed random variables. The improvements we get concern the rate function which is, as expected, the Legendre transform of the suprema of the log-Laplace transform of the pushforward measure by the functions of the considered class (up to an additional corrective term). Our approach is based on a decomposition in martingale together with some comparison inequalities.

Mots clés: Concentration inequalities; Empirical processes; Large deviations; Comparison inequalities; Martingale method

Domaines: Mathématiques [math]; Probabilités [math.PR]

Antoine Marchina. About the rate function in concentration inequalities for suprema of bounded empirical processes. Stochastic Processes and their Applications, 2019, 129 (10), pp.3967-3980. ⟨10.1016/j.spa.2018.11.010⟩. ⟨hal-01587060v3⟩