Concentration 0nequalities for Statistical Inference

• 来源期刊: 数学研究通讯
• 年，卷（期）: 2021,（1）
• 页码范围: 1-85
• 页数: 85页
• 语种: 英文
• DOI: 10.4208/cmr.2020-0041

摘要

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings,from distribution-free to distribution-dependent,from sub-Gaussian to sub-exponential,sub-Gamma,and sub-Weibull random vari-ables,and from the mean to the maximum concentration.This review pro-vides results in these settings with some fresh new results.Given the increas-ing popularity of high-dimensional data and inference,results in the context of high-dimensional linear and Poisson regressions are also provided.We aim to illustrate the concentration inequalities with known constants and to improve existing bounds with sharper constants.