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February 2021 Cramér-type moderate deviation theorems for nonnormal approximation
Qi-Man Shao, Mengchen Zhang, Zhuo-Song Zhang
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Ann. Appl. Probab. 31(1): 247-283 (February 2021). DOI: 10.1214/20-AAP1589


A Cramér-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 Cramér-type moderate result using Stein’s method when the limiting was a normal distribution. In this paper, Cramér-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 Cramér-type moderate deviation theorem is obtained for the general Curie–Weiss model and the imitative monomer-dimer mean-field model.


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Qi-Man Shao. Mengchen Zhang. Zhuo-Song Zhang. "Cramér-type moderate deviation theorems for nonnormal approximation." Ann. Appl. Probab. 31 (1) 247 - 283, February 2021.


Received: 1 September 2019; Revised: 1 February 2020; Published: February 2021
First available in Project Euclid: 8 March 2021

Digital Object Identifier: 10.1214/20-AAP1589

Primary: 60F10
Secondary: 60F05

Keywords: Curie–Weiss model , imitative monomer-dimer mean-field model , Moderate deviation , nonnormal approximation , Stein’s method

Rights: Copyright © 2021 Institute of Mathematical Statistics

Vol.31 • No. 1 • February 2021
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