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arXiv · 2011.02258

Concentration Inequalities for Statistical Inference

Huiming Zhang·Song Xi Chen
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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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BibTeXRIS

Huiming Zhang, Song Xi Chen. 2020-11-04. Concentration Inequalities for Statistical Inference. https://doi.org/10.4208/cmr.2020-0041

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