Normal approximation under local dependence. (English) Zbl 1048.60020

This paper is concerned with normal approximation under local dependence by using Stein’s method. Local dependence roughly means that certain subsets of the random variables are independent of those outside their respective “neighborhoods”. No structure on the index set is assumed. Both uniform and nonuniform error bounds of the Berry-Esseen type are obtained and shown to be more general or sharper than many existing results in the literature.


60F05 Central limit and other weak theorems
60G60 Random fields
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