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On the Accuracy in a Combinatorial Central Limit Theorem: The Characteristic Function Method
Theory of Probability and Its Applications ( IF 0.5 ) Pub Date : 2022-05-05 , DOI: 10.1137/s0040585x97t990794
B. Roos

Theory of Probability &Its Applications, Volume 67, Issue 1, Page 118-139, May 2022.
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.


中文翻译:

关于组合中心极限定理的精度:特征函数法

概率理论及其应用,第 67 卷,第 1 期,第 118-139 页,2022 年 5 月
。本文的目的是提出一个新的证明版本的 Berry-Esseen 类型不等式的 Bolthausen [Z. 瓦尔施。版本。Gebiete, 66 (1984), pp. 379--386]。文献已经提供了几个使用 Stein 方法变体的证明。特征函数法也被应用,但只导致较弱的结果。在本文中,我们展示了如何通过使用复杂矩阵的永久物的新恒等式以及最近证明的近似分布特征函数的不等式来克服这种方法的困难。
更新日期:2022-05-06
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