Open Access
2020 Poincaré inequalities and normal approximation for weighted sums
S.G. Bobkov, G.P. Chistyakov, F. Götze
Electron. J. Probab. 25: 1-31 (2020). DOI: 10.1214/20-EJP549


Under Poincaré-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on improved concentration inequalities on high-dimensional Euclidean spheres, the results extend and refine previous results to non-symmetric models.


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S.G. Bobkov. G.P. Chistyakov. F. Götze. "Poincaré inequalities and normal approximation for weighted sums." Electron. J. Probab. 25 1 - 31, 2020.


Received: 12 February 2020; Accepted: 11 November 2020; Published: 2020
First available in Project Euclid: 23 December 2020

Digital Object Identifier: 10.1214/20-EJP549

Primary: 60E , 60FEJP

Keywords: central limit theorem , Normal approximation , typical distributions

Vol.25 • 2020
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