Open Access
January 2013 From Stein identities to moderate deviations
Louis H. Y. Chen, Xiao Fang, Qi-Man Shao
Ann. Probab. 41(1): 262-293 (January 2013). DOI: 10.1214/12-AOP746


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.


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Louis H. Y. Chen. Xiao Fang. Qi-Man Shao. "From Stein identities to moderate deviations." Ann. Probab. 41 (1) 262 - 293, January 2013.


Published: January 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1275.60029
MathSciNet: MR3059199
Digital Object Identifier: 10.1214/12-AOP746

Primary: 60F10
Secondary: 60F05

Keywords: anti-voter model , Berry–Esseen bounds , combinatorial central limit theorem , Curie–Weiss model , Dependent random variables , Exchangeable pairs , general system of binary codes , Moderate deviations , Stein identity , Stein’s method , zero-bias coupling

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 1 • January 2013
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