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

TL;DR

This paper introduces a novel unbounded exchangeable pair approach to derive non-uniform Berry-Esseen bounds for normal and nonnormal approximations, applicable to quadratic forms, Curie-Weiss model, and independence tests.

Contribution

It presents a new technique that avoids reliance on concentration inequalities, enabling bounds under lower moment conditions for various probabilistic models.

Findings

Non-uniform bounds for independence tests under 6th moment condition

Applicable to quadratic forms and Curie-Weiss model

Improves moment condition requirements compared to previous methods

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.