CRAMER-TYPE MODERATE DEVIATION THEOREMS FOR NONNORMAL APPROXIMATION

• 成果类型: Article
• 署名作者: Shao, Qi-Man; Zhang, Mengchen; Zhang, Zhuo-Song
• 署名单位: Southern University of Science & Technology; Chinese University of Hong Kong; Hong Kong University of Science & Technology; National University of Singapore
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1589
• 发表日期: 2021
• 页码: 247-283
• 关键词: steins method; statistical-theory

摘要

A Cramer-type moderate deviation theorem quantifies the relative error of the tail probability approximation. It provides a criterion whether the limiting tail probability can be used to estimate the tail probability under study. Chen, Fang and Shao (2013) obtained a general Cramer-type moderate result using Stein's method when the limiting was a normal distribution. In this paper, Cramer-type moderate deviation theorems are established for nonnormal approximation under a general Stein identity, which is satisfied via the exchangeable pair approach and Stein's coupling. In particular, a Cramer-type moderate deviation theorem is obtained for the general Curie-Weiss model and the imitative monomer-dimer mean-field model.