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.
View on arXiv@article{zhang2025_2011.02258,
title={ Concentration Inequalities for Statistical Inference },
author={ Huiming Zhang and Song Xi Chen },
journal={arXiv preprint arXiv:2011.02258},
year={ 2025 }
}