Poincaré inequalities and normal approximation for weighted sums

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

doi:10.1214/20-EJP549

Poincaré inequalities and normal approximation for weighted sums

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

Mathematics

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

3 Scopus citations

Abstract

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.

Original language	English (US)
Article number	155
Pages (from-to)	1-31
Number of pages	31
Journal	Electronic Journal of Probability
Volume	25
DOIs	https://doi.org/10.1214/20-EJP549
State	Published - 2020

Bibliographical note

Funding Information:
*Research was supported by SFB 1283, Simons Foundation, and NSF grant DMS-1855575. †School of Mathematics, University of Minnesota. E-mail: bobkov@math.umn.edu ‡Faculty of Mathematics, University of Bielefeld. E-mail: chistyak@math.uni-bielefeld.de §Faculty of Mathematics, University of Bielefeld. E-mail: goetze@math.uni-bielefeld.de

Publisher Copyright:
© 2020, Institute of Mathematical Statistics. All rights reserved.

Keywords

Central limit theorem
Normal approximation
Typical distributions

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abstract = "Under Poincar{\'e}-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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year = "2020",

doi = "10.1214/20-EJP549",

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AU - Bobkov, S. G.

AU - Chistyakov, G. P.

AU - Götze, F.

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PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Normal approximation

KW - Typical distributions

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JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 155

ER -

Poincaré inequalities and normal approximation for weighted sums

Abstract

Bibliographical note

Keywords

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