Normal approximation under local dependence

2004/10/05 by Louis H. Y. Chen, Qi-Man Shao · 2 citations
Mathematics · #math.PR #msc:60F05 #msc:60G60.

paper · pdf · doi:10.1214/009117904000000450

published as Annals of Probability 2004, Vol. 32, No. 3A, 1985-2028 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000450

arxiv created 2004/10/05 · arxiv updated 2009/12/01

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.

Cited by

• Controlling the false discovery rate under a non-parametric graphical dependence model
• Non-uniform bounds for non-normal approximation via Stein's method with applications to the Curie--Weiss model and the imitative monomer-dimer model

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• Berry--Esseen bounds for self-normalized sums of local dependent random variables
• Multivariate Normal Approximation by Stein's Method: The Concentration Inequality Approach
• Berry-Esseen bounds in local limit theorems
• Stein's method via induction
• Non-uniform bounds for non-normal approximation via Stein's method with applications to the Curie--Weiss model and the imitative monomer-dimer model