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 -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.
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