Normal approximation under local dependence
Louis H. Y. Chen and Qi-Man Shao
Source: Ann. Probab. Volume 32, Number 3
(2004), 1985-2028.
Abstract
We establish both uniform and nonuniform error bounds of the Berry–Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper than many existing ones in the literature. The proofs couple Stein’s method with the concentration inequality approach.
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Keywords: Stein’s method; normal approximation; local dependence; concentration inequality; uniform Berry–Esseen bound; nonuniform Berry–Esseen bound; random field
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1089808417
Digital Object Identifier: doi:10.1214/009117904000000450
Mathematical Reviews number (MathSciNet): MR2073183
Zentralblatt MATH identifier: 1048.60020
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