Concentration Inequalities for Statistical Inference
H. Zhang, and S. Chen. (2020)cite arxiv:2011.02258Comment: 55 pages. Communications in Mathematical Research. (to appear, invited review paper).
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.
Description
[2011.02258] Concentration Inequalities for Statistical Inference
%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
}