Title
An isometric study of the LindebergFeller central limit theorem via Steins method An isometric study of the LindebergFeller central limit theorem via Steins method
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Journal of mathematical analysis and applications. - New York, N.Y.
Volume/pages
405(2013) :2 , p. 484-498
ISSN
0022-247X
ISI
000320288500014
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We use Steins method to prove a generalization of the LindebergFeller CLT providing an upper and a lower bound for the superior limit of the Kolmogorov distance between a normally distributed random variable and the rowwise sums of a rowwise independent triangular array of random variables which is asymptotically negligible in the sense of Feller. A natural example shows that the upper bound is of optimal order. The lower bound improves a result by Andrew Barbour and Peter Hall.
E-info
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