Recent development in high-dimensional statistical inference has necessitated concentration inequalities for a broader range of random variables. We focus on sub-Weibull random variables, which extend sub-Gaussian or sub-exponential random variables to allow heavy-tailed distributions. This paper presents concentration inequalities for independent sub-Weibull random variables with finite Generalized Bernstein-Orlicz norms, providing generalized Bernstein's inequalities and Rosenthal-type moment bounds. The tightness of the proposed bounds is shown through lower bounds of the concentration inequalities obtained via the Paley-Zygmund inequality. The results are applied to a graphical model inference problem, improving previous sample complexity bounds.

翻译：高维统计推断的最新进展要求对更广泛随机变量建立集中不等式。本文聚焦于次Weibull随机变量——这类变量将次高斯或次指数随机变量扩展至可容纳重尾分布的情形。针对具有有限广义Bernstein-Orlicz范数的独立次Weibull随机变量，本文提出了集中不等式，给出了广义Bernstein不等式和Rosenthal型矩界。通过利用Paley-Zygmund不等式获得的集中不等式下界，证明了所提界的最优性。将结果应用于图模型推断问题，改进了先前的样本复杂度界。