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May 2020 Normal approximation for weighted sums under a second-order correlation condition
S. G. Bobkov, G. P. Chistyakov, F. Götze
Ann. Probab. 48(3): 1202-1219 (May 2020). DOI: 10.1214/19-AOP1388

Abstract

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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S. G. Bobkov. G. P. Chistyakov. F. Götze. "Normal approximation for weighted sums under a second-order correlation condition." Ann. Probab. 48 (3) 1202 - 1219, May 2020. https://doi.org/10.1214/19-AOP1388

Information

Received: 1 October 2018; Revised: 1 June 2019; Published: May 2020
First available in Project Euclid: 17 June 2020

zbMATH: 07226358
MathSciNet: MR4112712
Digital Object Identifier: 10.1214/19-AOP1388

Subjects:
Primary: 60E, 60F

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • May 2020
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