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.
Funding Statement
It was partially supported by Hong Kong Research Grants Council GRF 14304917. This research was also partially supported by the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers CE140100049 and by Singapore Ministry of Education Academic Research Fund MOE 2018-T2-076.
Acknowledgements
The author would like to thank the associate editor and two referees for their valuable comments which led to substantial improvement in the presentation of this paper. The author would also like to thank Qi-Man Shao for his comments. Part of the paper was completed during the period of my visit at the Chinese University of Hong Kong.
Citation
Zhuo-Song Zhang. "Cramér-type moderate deviation of normal approximation for unbounded exchangeable pairs." Bernoulli 29 (1) 274 - 299, February 2023. https://doi.org/10.3150/21-BEJ1457
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