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

Author

Listed:
  • Maximilian Janisch

    (Universität Zürich)

  • Thomas Lehéricy

    (Universität Zürich
    Institut für Physik, Universität Zürich)

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.

Suggested Citation

  • Maximilian Janisch & Thomas Lehéricy, 2024. "Berry–Esseen-Type Estimates for Random Variables with a Sparse Dependency Graph," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3627-3653, November.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:4:d:10.1007_s10959-024-01363-z
    DOI: 10.1007/s10959-024-01363-z
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