Berry--Esseen bounds for generalized U statistics

2021/04/08 by Zhuo-Song Zhang, Zhang, Zhuo-Song · 1 citation
Mathematics · #60F05 #FOS: Mathematics #Limits and Structures in Graph Theory #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2104.03479

openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish optimal Berry--Esseen bounds for the generalized U-statistics. The proof is based on a new Berry--Esseen theorem for exchangeable pair approach by Stein's method under a general linearity condition setting. As applications, an optimal convergence rate of the normal approximation for subgraph counts in Erdös--Rényi graphs and graphon-random graph is obtained.

Citations

• Normal approximation for sums of discrete U-statistics - application to Kolmogorov bounds in random subgraph counting

Cited by

• Asymptotic Normality of Subgraph Counts in Sparse Inhomogeneous Random Graphs

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