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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 1, Pages 150–175
DOI: https://doi.org/10.4213/tvp5412 (Mi tvp5412) 		 
On the accuracy in a combinatorial central limit theorem: the characteristic function method

B. Roos

FB IV – Department of Mathematics, University of Trier, Trier, Germany
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DOI: https://doi.org/10.4213/tvp5412
Abstract: The aim of this paper is to present a new proof of an explicit version of the Berry–Esseen type inequality of Bolthausen [Z. Wahrsch. Verw. Gebiete, 66 (1984), pp. 379–386]. The literature already provides several proofs using variants of Stein's method. The characteristic function method has also been applied but led only to weaker results. In this paper, we show how to overcome the difficulties of this method by using a new identity for permanents of complex matrices in combination with a recently proved inequality for the characteristic function of the approximated distribution.
Keywords: approximation of permanents, characteristic function method, combinatorial central limit theorem, permanental identity, sampling without replacement.
Received: 24.04.2020
Revised: 26.10.2020
Accepted: 20.10.2020
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 1, Pages 118–139
DOI: https://doi.org/10.1137/S0040585X97T990794
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. Roos, “On the accuracy in a combinatorial central limit theorem: the characteristic function method”, Teor. Veroyatnost. i Primenen., 67:1 (2022), 150–175; Theory Probab. Appl., 67:1 (2022), 118–139
Citation in format AMSBIB
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\pages 150--175
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\transl
\jour Theory Probab. Appl.
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\pages 118--139
\crossref{https://doi.org/10.1137/S0040585X97T990794}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85131046098}
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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