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

School of Mathematics

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

4 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: [email protected] ‡Faculty of Mathematics, University of Bielefeld. E-mail: [email protected] §Faculty of Mathematics, University of Bielefeld. E-mail: [email protected]

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

Keywords

Central limit theorem
Normal approximation
Typical distributions

Publisher link

10.1214/20-EJP549

Find It

Find It at U of M Libraries

Cite this

@article{4efce8958b204e7b9432febf8cdc99ef,

title = "Poincar{\'e} inequalities and normal approximation for weighted sums",

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.",

keywords = "Central limit theorem, Normal approximation, Typical distributions",

author = "Bobkov, {S. G.} and Chistyakov, {G. P.} and F. G{\"o}tze",

note = "Funding Information: *Research was supported by SFB 1283, Simons Foundation, and NSF grant DMS-1855575. †School of Mathematics, University of Minnesota. E-mail: [email protected] ‡Faculty of Mathematics, University of Bielefeld. E-mail: [email protected] §Faculty of Mathematics, University of Bielefeld. E-mail: [email protected] Publisher Copyright: {\textcopyright} 2020, Institute of Mathematical Statistics. All rights reserved.",

year = "2020",

doi = "10.1214/20-EJP549",

language = "English (US)",

volume = "25",

pages = "1--31",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Poincaré inequalities and normal approximation for weighted sums

AU - Bobkov, S. G.

AU - Chistyakov, G. P.

AU - Götze, F.

N1 - Funding Information: *Research was supported by SFB 1283, Simons Foundation, and NSF grant DMS-1855575. †School of Mathematics, University of Minnesota. E-mail: [email protected] ‡Faculty of Mathematics, University of Bielefeld. E-mail: [email protected] §Faculty of Mathematics, University of Bielefeld. E-mail: [email protected] Publisher Copyright: © 2020, Institute of Mathematical Statistics. All rights reserved.

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

UR - http://www.scopus.com/inward/record.url?scp=85098877204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85098877204&partnerID=8YFLogxK

U2 - 10.1214/20-EJP549

DO - 10.1214/20-EJP549

M3 - Article

AN - SCOPUS:85098877204

SN - 1083-6489

VL - 25

SP - 1

EP - 31

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

Publisher link

Find It

Other files and links

Fingerprint

Cite this