S. G. Bobkov, G. P. Chistyakov, F. Götze
Published 2019-06-21Version 1
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.
Poincaré Inequalities and Normal Approximation for Weighted Sums
A multivariate CLT for <<typical>> weighted sums with rate of convergence of order O(1/n)
$L^1$ bounds in normal approximation
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