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

2019/09/30 by Dali Liu, Liu, Dali, Zheng Li +5
Materials Science · Mathematics · #FOS: Mathematics #Graph theory and applications #Nanocluster Synthesis and Applications #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1909.13477

openalex publication_date 2019/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citecls1, 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 \citecs2 requires 24th moment condition.

Citations

• Statistical Challenges with High Dimensionality: Feature Selection in Knowledge Discovery
• A short survey of Stein's method

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