Geodesic
On the accuracy in a~combinatorial central limit theorem: the characteristic function method
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 150-175

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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. 
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B. Roos. On the accuracy in a~combinatorial central limit theorem: the characteristic function method. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 150-175. http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a8/