@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 = {<p style="text-align: justify;">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.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2020-0041},
url = {http://global-sci.org/intro/article_detail/cmr/18625.html}
}