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Title
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An isometric study of the LindebergFeller central limit theorem via Steins method
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Journal of mathematical analysis and applications. - New York, N.Y.
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Publication
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New York, N.Y.
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2013
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ISSN
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0022-247X
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DOI
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10.1016/J.JMAA.2013.04.012
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Volume/pages
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405
:2
(2013)
, p. 484-498
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ISI
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000320288500014
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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