Berry–Esseen-Type Estimates for Random Variables with a Sparse Dependency Graph

Abstract

We obtain Berry–Esseen-type bounds for the sum of random variables with a dependency graph and uniformly bounded moments of order δ∈(2,∞]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \\in (2,\\infty ]$$\\end{document} using a Fourier transform approach. Our bounds improve the state-of-the-art obtained by Stein’s method in the regime where the degree of the dependency graph is large.