Cramér-type moderate deviation of normal approximation for unbounded exchangeable pairs

2019/01/28 by Zhuo-Song Zhang, Zhang, Zhuo-Song · 1 citation
Mathematics · #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Primary 60F10 #Probability (math.PR) #Random Matrices and Applications #secondary 60G60

paper · pdf · doi:10.48550/arxiv.1901.09526

openalex publication_date 2019/01/28 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cramér-type moderate deviation theorem of normal approximation for unbounded exchangeable pairs. As applications, Cramér-type moderate deviation theorems for the sums of local statistics and general Curie--Weiss model are obtained.

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• Non-uniform bounds for non-normal approximation via Stein's method with applications to the Curie--Weiss model and the imitative monomer-dimer model

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