Concentration Inequalities for Statistical Inference
This is an incremental review that compiles and refines concentration inequalities for researchers in statistics and machine learning dealing with high-dimensional data.
The paper reviews concentration inequalities for statistical inference, providing results across various settings and improving existing bounds with sharper constants.
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.