Normal approximation for weighted sums under a second-order correlation condition

S. G. Bobkov; G. P. Chistyakov; F. Götze

doi:10.1214/19-AOP1388

Normal approximation for weighted sums under a second-order correlation condition

S. G. Bobkov, G. P. Chistyakov, F. Götze

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1202-1219
Number of pages	18
Journal	Annals of Probability
Volume	48
Issue number	3
DOIs	https://doi.org/10.1214/19-AOP1388
State	Published - 2020

Bibliographical note

Funding Information:
Acknowledgments. The authors would like to thank the two referees for careful reading of the manuscript and valuable comments. This work was supported by NSF Grant DMS-1855575, the Simons Foundation and CRC 1283 at Bielefeld University.

Publisher Copyright:
© Institute of Mathematical Statistics, 2020.

Keywords

Normal approximation
Sudakov's typical distributions

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AU - Bobkov, S. G.

AU - Chistyakov, G. P.

AU - Götze, F.

N1 - Funding Information: Acknowledgments. The authors would like to thank the two referees for careful reading of the manuscript and valuable comments. This work was supported by NSF Grant DMS-1855575, the Simons Foundation and CRC 1283 at Bielefeld University. Publisher Copyright: © Institute of Mathematical Statistics, 2020.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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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KW - Sudakov's typical distributions

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Normal approximation for weighted sums under a second-order correlation condition

Abstract

Bibliographical note

Keywords

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