@Article{CMR-37-1, author = {Zhang , Huiming and Chen , Songxi}, title = {Concentration Inequalities for Statistical Inference}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {1}, pages = {1--85}, abstract = {

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 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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0041}, url = {http://global-sci.org/intro/article_detail/cmr/18625.html} }