Approximate Central Limit Theorems

Ben Berckmoes () and Geert Molenberghs ()
Additional contact information
Ben Berckmoes: Universiteit Antwerpen
Geert Molenberghs: Universiteit Hasselt

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1590-1605

Abstract: Abstract We refine the classical Lindeberg–Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parameterized Prokhorov distances in terms of a Lindeberg index. We thus obtain more general approximate central limit theorems, which roughly state that the row-wise sums of a triangular array are approximately asymptotically normal if the array approximately satisfies Lindeberg’s condition. This allows us to continue to provide information in nonstandard settings in which the classical central limit theorem fails to hold. Stein’s method plays a key role in the development of this theory.

Keywords: Kolmogorov metric; Lindeberg–Feller central limit theorem; Lindeberg index; Prokhorov metric; Stein’s method; Wasserstein metric; 60F05 (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-017-0744-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0744-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-017-0744-6

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().