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Non-uniform Berry-Esseen Bound by Unbounded Exchangeable Pair Approach
Dali Liu, Zheng Li, Hanchao Wang, Zengjing Chen · 2019-09-30 · via math.ST updates on arXiv.org

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.

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