TY - JOUR
T1 - Concentration Inequalities for Statistical Inference
AU - Zhang , Huiming
AU - Chen , Songxi
JO - Communications in Mathematical Research 
VL - 1
SP - 1
EP - 85
PY - 2021
DA - 2021/02
SN - 37
DO - http://doi.org/10.4208/cmr.2020-0041
UR - https://global-sci.org/intro/article_detail/cmr/18625.html
KW - Constants-specified inequalities, sub-Weibull random variables, heavy-tailed
distributions, high-dimensional estimation and testing, finite-sample theory, random matrices.
AB - <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>