This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in awide range of settings,fromdistribution-free to distribution-dependent,from...This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in awide range of settings,fromdistribution-free to distribution-dependent,from sub-Gaussian to sub-exponential,sub-Gamma,and sub-Weibull random variables,and from the mean to the maximum concentration.This review provides results in these settings with some fresh new results.Given the increasing 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.展开更多
基金funded by National Natural Science Foundation of China(Grants 92046021,12071013,12026607,71973005)LMEQF at Peking University.
文摘This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in awide range of settings,fromdistribution-free to distribution-dependent,from sub-Gaussian to sub-exponential,sub-Gamma,and sub-Weibull random variables,and from the mean to the maximum concentration.This review provides results in these settings with some fresh new results.Given the increasing 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.
