Vector-valued statistics of binomial processes: Berry–Esseen bounds in the convex distance

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1897

Mikołaj J. Kasprzak, Giovanni Peccati

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引用次数: 1

Abstract

We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions, holding in every dimension. Such a finding constitutes a substantial extension of the one-dimensional bounds deduced in Chatterjee (Ann. Probab. 36 (2008) 1584–1610) and Lachièze-Rey and Peccati (Ann. Appl. Probab. 27 (2017) 1992–2031), as well as of the multidimensional bounds for smooth test functions and indicators of rectangles derived, respectively, in Dung (Acta Math. Hungar. 158 (2019) 173–201), and Fang and Koike (Ann. Appl. Probab. 31 (2021) 1660–1686). Our techniques involve the use of Stein’s method, combined with a suitable adaptation of the recursive approach inaugurated by Schulte and Yukich (Electron. J. Probab. 24 (2019) 1–42): this yields rates of converge that have a presumably optimal dependence on the sample size. We develop several applications of a geometric nature, among which is a new collection of multidimensional quantitative limit theorems for the intrinsic volumes associated with coverage processes in Euclidean spaces.

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二项过程的向量值统计:凸距上的Berry-Esseen界

研究了随机元素的向量值泛函的分布与高斯向量分布的差异。我们的主要贡献是两个分布之间凸距离的显式边界，在每个维度上都成立。这样的发现构成了在查特吉(安。Probab. 36(2008) 1584-1610)和lachi - rey和Peccati (Ann。达成。Probab. 27(2017) 1992-2031)，以及分别推导出的光滑测试函数和矩形指标的多维界限(数学学报)。匈牙利，158(2019)173-201)，方和小池(安。达成。约31(2021)1660-1686)。我们的技术包括使用Stein的方法，结合舒尔特和尤基奇(Electron)开创的递归方法的适当适应。J. Probab. 24(2019) 1-42):这产生的收敛率可能对样本量具有最佳依赖性。我们开发了几个几何性质的应用，其中包括欧几里得空间中与覆盖过程相关的内在体积的多维定量极限定理的新集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.