The Annals of Probability

From Stein identities to moderate deviations

Louis H. Y. Chen, Xiao Fang, and Qi-Man Shao

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Stein’s method is applied to obtain a general Cramér-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also applied to a combinatorial central limit theorem, a general system of binary codes, the anti-voter model on a complete graph, and the Curie–Weiss model. A general moderate deviation result for independent random variables is also proved.

Article information

Ann. Probab., Volume 41, Number 1 (2013), 262-293.

First available in Project Euclid: 23 January 2013

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60F05: Central limit and other weak theorems

Stein’s method Stein identity moderate deviations Berry–Esseen bounds zero-bias coupling exchangeable pairs dependent random variables combinatorial central limit theorem general system of binary codes anti-voter model Curie–Weiss model


Chen, Louis H. Y.; Fang, Xiao; Shao, Qi-Man. From Stein identities to moderate deviations. Ann. Probab. 41 (2013), no. 1, 262--293. doi:10.1214/12-AOP746.

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