Berry-Esseen-type estimates for random variables with a sparse dependency graph

2022/12/05 by Janisch, Maximilian, Lehéricy, Thomas
#60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2212.02590

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,∞] using a Fourier transform approach. Our bounds improve the state-of-the-art in the regime where the degree of the dependency graph is large. As a Corollary of our results, we obtain a Central Limit Theorem for random variables with a sparse dependency graph that are uniformly bounded in L^δ for some δ∈(2,∞].

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