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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Marchina, Antoine¹ 

[1] Univ Paris Saclay, UVSQ, CNRS, Lab Math Versailles, F-78035 Versailles, France

关键词: Concentration inequality;    Empirical process;    Large deviation bandwidth;    Comparison inequality;    Martingale method;   

DOI  :  10.1016/j.spa.2018.11.010

来源: Elsevier

【 摘 要 】

We provide new deviation inequalities in the large deviations bandwidth 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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free