Year: 2021
Author: Huiming Zhang, Songxi Chen
Communications in Mathematical Research , Vol. 37 (2021), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0041
Communications in Mathematical Research , Vol. 37 (2021), Iss. 1 : pp. 1–85
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 85
Keywords: Constants-specified inequalities sub-Weibull random variables heavy-tailed distributions high-dimensional estimation and testing finite-sample theory random matrices.