Concentration around the mean for maxima of empirical processes

2005/05/01 by Thierry Klein, T. Klein, E. Rio +1 · 8 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Statistical Methods and Inference #math.PR #msc:60E15 #msc:60F10.

paper · pdf · doi:10.1214/009117905000000044

published as Annals of Probability 2005, Vol. 33, No. 3, 1060-1077 · Published at http://dx.doi.org/10.1214/009117905000000044 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/05/01 · arxiv created 2005/06/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give optimal constants in Talagrand’s concentration inequalities for maxima of empirical processes associated to independent and eventually nonidentically distributed random variables. Our approach is based on the entropy method introduced by Ledoux.

Cited by

• On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms
• Nonparametric Estimation For Censored Circular Data
• Statistical analysis of Wasserstein GANs with applications to time series forecasting
• Multiplicative deconvolution estimator based on a ridge approach
• Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective
• Adaptive non-parametric estimation in the presence of dependence
• Exact Matrix Completion via Convex Optimization
• A probabilistic approach to the leader problem in random graphs

Related

• Concentration inequalities for Poisson point processes with application to adaptive intensity estimation
• Gaussian martingale inequality applies to random functions and maxima of empirical processes
• Concentration of measure without independence: a unified approach via the martingale method
• Concentration of Measure Techniques and Applications
• Finite-sample concentration of the empirical relative entropy around its mean