The Annals of Probability

A new method of normal approximation

Sourav Chatterjee

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Abstract

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.

Article information

Source
Ann. Probab., Volume 36, Number 4 (2008), 1584-1610.

Dates
First available in Project Euclid: 29 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aop/1217360979

Digital Object Identifier
doi:10.1214/07-AOP370

Mathematical Reviews number (MathSciNet)
MR2435859

Zentralblatt MATH identifier
1159.62009

Subjects
Primary: 60F05: Central limit and other weak theorems 60B10: Convergence of probability measures 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]

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

Citation

Chatterjee, Sourav. A new method of normal approximation. Ann. Probab. 36 (2008), no. 4, 1584--1610. doi:10.1214/07-AOP370. https://projecteuclid.org/euclid.aop/1217360979


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