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

We obtain Berry-Esseen-type bounds for the sum of random variables with a dependency graph and uniformly bounded moments of order delta is an element of(2,infinity]\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.