论文标题
统计推断的浓度不平等
Concentration Inequalities for Statistical Inference
论文作者
论文摘要
本文综述了浓度不平等的综述，这些不平等广泛用于数学统计的非反应分析中，从无分布到分布依赖性，从高斯次级，次指数，亚伽玛和亚及以下随机变量以及从平均值到最大浓度。这篇综述为这些设置提供了一些新的新结果。鉴于高维数据和推断的日益普及，还提供了高维线性和泊松回归的背景下的结果。我们旨在说明具有已知常数的集中度不平等，并用更清晰的常数提高现有界限。
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.
