2023/02/08 by Heejong Bong, Arun Kumar Kuchibhotla, Bong, Heejong +1 · 1 citation
Mathematics · #60E15 (Primary) 60B20 #60G50 #62E22 (Secondary) #Advanced Statistical Methods and Models #Applied mathematics #Bernstein inequalities #Computer science #Exponential function #FOS: Mathematics #Gaussian #Inequality #Inference #Mathematical analysis #Mathematics #Norm (philosophy) #Probability (math.PR) #Random variable #Statistical Methods and Inference #Statistics #Statistics Theory (math.ST) #Weibull distribution
paper · pdf · doi:10.48550/arxiv.2302.03850
openalex publication_date 2023/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.