## The Annals of Probability

### Normal approximation under local dependence

#### 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.

#### Article information

Source
Ann. Probab., Volume 32, Number 3 (2004), 1985-2028.

Dates
First available in Project Euclid: 14 July 2004

https://projecteuclid.org/euclid.aop/1089808417

Digital Object Identifier
doi:10.1214/009117904000000450

Mathematical Reviews number (MathSciNet)
MR2073183

Zentralblatt MATH identifier
1048.60020

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G60: Random fields

#### Citation

Chen, Louis H. Y.; Shao, Qi-Man. Normal approximation under local dependence. Ann. Probab. 32 (2004), no. 3, 1985--2028. doi:10.1214/009117904000000450. https://projecteuclid.org/euclid.aop/1089808417

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