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Matematicheskie Trudy, 2016, Volume 19, Number 2, Pages 170–199
DOI: https://doi.org/10.17377/mattrudy.2016.19.207 (Mi mt310) 		 
This article is cited in 5 scientific papers (total in 7 papers)

On the real accuracy of approximation in the central limit theorem. II

V. V. Senatov

Lomonosov Moscow State University, Moscow, Russia
Full-text PDF (297 kB) Citations (7)
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DOI: https://doi.org/10.17377/mattrudy.2016.19.207
Abstract: In the present article, we obtain new explicit estimates for accuracy of approximation in the central limit theorem (CLT). We construct these approximations with the use of asymptotic expansions. We compare the estimates with the real accuracy of approximation for a specific distribution. We also discuss the following question: Why the estimate from the Berry–Esseen theorem cannot catch even the order of proximity of distributions in the CLT?
Key words: central limit theorem, accuracy of approximation, asymptotic expansions, Berry–Esseen theorem.
Received: 28.02.2016
English version:
Siberian Advances in Mathematics, 2017, Volume 27, Issue 2, Pages 133–152
DOI: https://doi.org/10.3103/S1055134417020043
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: V. V. Senatov, “On the real accuracy of approximation in the central limit theorem. II”, Mat. Tr., 19:2 (2016), 170–199; Siberian Adv. Math., 27:2 (2017), 133–152
Citation in format AMSBIB
\Bibitem{Sen16}
\by V.~V.~Senatov
\paper On the real accuracy of approximation in the central limit theorem. II
\jour Mat. Tr.
\yr 2016
\vol 19
\issue 2
\pages 170--199
\mathnet{http://mi.mathnet.ru/mt310}
\crossref{https://doi.org/10.17377/mattrudy.2016.19.207}
\elib{https://elibrary.ru/item.asp?id=27258783}
\transl
\jour Siberian Adv. Math.
\yr 2017
\vol 27
\issue 2
\pages 133--152
\crossref{https://doi.org/10.3103/S1055134417020043}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019980076}
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    This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    References:71
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