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Normal Approximation for Weighted Sums under a Second Order Correlation Condition

Probability 2019-06-24 v1

Abstract

Under correlation-type conditions, we derive an upper bound of order (logn)/n(\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.

Keywords

Cite

@article{arxiv.1906.09063,
  title  = {Normal Approximation for Weighted Sums under a Second Order Correlation Condition},
  author = {S. G. Bobkov and G. P. Chistyakov and F. Götze},
  journal= {arXiv preprint arXiv:1906.09063},
  year   = {2019}
}
R2 v1 2026-06-23T09:59:49.129Z