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July 2008 A new method of normal approximation
Sourav Chatterjee
Ann. Probab. 36(4): 1584-1610 (July 2008). DOI: 10.1214/07-AOP370


We introduce a new version of Stein’s method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance must be bounded has an explicit formula that makes it possible to carry out the program more easily. As an application, we derive a general CLT for functions that are obtained as combinations of many local contributions, where the definition of “local” itself depends on the data. Several examples are given, including the solution to a nearest-neighbor CLT problem posed by P. Bickel.


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Sourav Chatterjee. "A new method of normal approximation." Ann. Probab. 36 (4) 1584 - 1610, July 2008.


Published: July 2008
First available in Project Euclid: 29 July 2008

zbMATH: 1159.62009
MathSciNet: MR2435859
Digital Object Identifier: 10.1214/07-AOP370

Primary: 60B10 , 60D05 , 60F05

Keywords: central limit theorem , coverage processes , nearest neighbors , Normal approximation , occupancy problems , Quadratic forms , Stein’s method

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 4 • July 2008
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