NORMAL APPROXIMATION FOR WEIGHTED SUMS UNDER A SECOND-ORDER CORRELATION CONDITION

Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Ap...

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Bibliographic Details
Published in:The Annals of probability 2020-05, Vol.48 (3), p.1202-1219
Main Authors: Bobkov, S. G., Chistyakov, G. P., Götze, F.
Format: Article
Language:English
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Summary:Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.
ISSN:0091-1798
2168-894X
DOI:10.1214/19-AOP1388