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 $$\delta \in (2,\infty ]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> 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.