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 Erdos̈–Rényi graphs and graphon-random graph is obtained.
Funding Statement
The research is partially supported by Singapore Ministry of Education Academic Research Fund MOE 2018-T2-076.
Acknowledgments
The author thank the editor and two referees for their valuable comments which led to substantial improvement in the presentation of the paper.
Citation
Zhuo-Song Zhang. "Berry–Esseen bounds for generalized U-statistics." Electron. J. Probab. 27 1 - 36, 2022. https://doi.org/10.1214/22-EJP860
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