Poincaré inequalities and normal approximation for weighted sums

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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Article number155
Pages (from-to)1-31
Number of pages31
JournalElectronic Journal of Probability
Volume25
DOIs
StatePublished - 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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