%0 Journal Article %1 zhang2020concentration %A Zhang, Huiming %A Chen, Song Xi %D 2020 %K bounds concentration inequality stats survey %T Concentration Inequalities for Statistical Inference %U http://arxiv.org/abs/2011.02258 %X 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.

@article{zhang2020concentration, 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.}, added-at = {2021-01-24T11:54:05.000+0100}, author = {Zhang, Huiming and Chen, Song Xi}, biburl = {https://www.bibsonomy.org/bibtex/2670f468d6146b191ab36b41885924f2f/kirk86}, description = {[2011.02258] Concentration Inequalities for Statistical Inference}, interhash = {67be0d5a5ee476c1d920b0e1086e8685}, intrahash = {670f468d6146b191ab36b41885924f2f}, keywords = {bounds concentration inequality stats survey}, note = {cite arxiv:2011.02258Comment: 55 pages. Communications in Mathematical Research. (to appear, invited review paper)}, timestamp = {2021-01-24T11:54:05.000+0100}, title = {Concentration Inequalities for Statistical Inference}, url = {http://arxiv.org/abs/2011.02258}, year = 2020 }