  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.
