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. Applications are illustrated on the example of log-concave probability measures.
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1202-1219
1202-1219
Inst Mathematical Statistics