G. Bobkov, S. et al., Normal approximation for weighted sums under a second-order correlation condition, Annals of probability (Online) , 48(3), 2020, pp. 1202-1219
Under correlation-type conditions, we derive an upper bound of order (logn)/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.