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Concentration Inequalities for Statistical Inference

Concentration Inequalities for Statistical Inference
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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.

Author Details

Huiming Zhang

Songxi Chen

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