Title
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Approximate central limit theorems
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Author
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Abstract
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We refine the classical LindebergFeller 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 Lindebergs condition. This allows us to continue to provide information in nonstandard settings in which the classical central limit theorem fails to hold. Steins method plays a key role in the development of this theory. |
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Language
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English
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Source (journal)
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Journal of theoretical probability. - New York
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Publication
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New York
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2018
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ISSN
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0894-9840
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DOI
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10.1007/S10959-017-0744-6
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Volume/pages
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31
:3
(2018)
, p. 1590-1605
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ISI
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000441304800012
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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