## The Annals of Probability

### From Stein identities to moderate deviations

#### Abstract

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

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

Dates
First available in Project Euclid: 23 January 2013

https://projecteuclid.org/euclid.aop/1358951987

Digital Object Identifier
doi:10.1214/12-AOP746

Mathematical Reviews number (MathSciNet)
MR3059199

Zentralblatt MATH identifier
1275.60029

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

#### Citation

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. https://projecteuclid.org/euclid.aop/1358951987

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