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Berry--Esseen bounds for generalized $U$ statistics

Probability 2021-04-09 v1

Abstract

In this paper, we establish optimal Berry--Esseen bounds for the generalized UU-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 Erd\"os--R\'enyi graphs and graphon-random graph is obtained.

Keywords

Cite

@article{arxiv.2104.03479,
  title  = {Berry--Esseen bounds for generalized $U$ statistics},
  author = {Zhuo-Song Zhang},
  journal= {arXiv preprint arXiv:2104.03479},
  year   = {2021}
}

Comments

34 pages

R2 v1 2026-06-24T00:56:47.687Z