Concentration Inequalities for Statistical Inference

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses mathematical statistics wide range settings, from distribution-free to distribution-dependent, sub-Gaussian sub-exponential, sub-Gamma, and sub-Weibull random variables, the mean maximum concentration. provides results these settings with some fresh new results. Given increasing popularity high-dimensional data inference, context linear Poisson regressions also provided. We aim illustrate known constants improve existing bounds sharper constants.