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

Maximilian Janisch () and Thomas Lehéricy ()
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Maximilian Janisch: Universität Zürich
Thomas Lehéricy: Universität Zürich

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3627-3653

Abstract: Abstract We obtain Berry–Esseen-type bounds for the sum of random variables with a dependency graph and uniformly bounded moments of order $$\delta \in (2,\infty ]$$ δ ∈ ( 2 , ∞ ] 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.

Keywords: Berry–Esseen; Cumulants; Dependency graph; 60F05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01363-z

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