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Non-uniform Berry-Esseen Bound by Unbounded Exchangeable Pair Approach

Statistics Theory 2019-12-24 v4 Statistics Theory

Abstract

In this paper, a new technique is introduced to obtain non-uniform Berry-Esseen bounds of normal and nonnormal approximation for unbounded exchangeable pairs. This technique does not rely on the concentration inequalities developed by Chen and Shao \cite{cls1, cls2} and can be applied to the quadratic forms, general Curie-Weiss model and an independence test. In particular, our non-uniform result about the independence test is under 6th moment condition, while the uniform bound in Chen and Shao \cite{cs2} requires 24th moment condition.

Keywords

Cite

@article{arxiv.1909.13477,
  title  = {Non-uniform Berry-Esseen Bound by Unbounded Exchangeable Pair Approach},
  author = {Dali Liu and Zheng Li and Hanchao Wang and Zengjing Chen},
  journal= {arXiv preprint arXiv:1909.13477},
  year   = {2019}
}

Comments

34pages, we reviewed the paper and corrected some typos. All comments are welcome

R2 v1 2026-06-23T11:29:49.012Z