About the constants in Talagrand's concentration inequalities for empirical processes

• 成果类型: Article
• 署名作者: Massart, P
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1019160263
• 发表日期: 2000
• 页码: 863-884
• 关键词: logarithmic sobolev inequalities

摘要

We propose some explicit values for the constants involved in the exponential concentration inequalities for empirical processes which are due to Talagrand. It has been shown by Ledoux that deviation inequalities for empirical processes could be obtained by iteration of logarithmic Sobolev type inequalities. Our approach follows closely that of Ledoux. The improvements that we get with respect to Ledoux's work are based on refinements of his entropy inequalities and computations.