论文标题
二项式过程的矢量值统计：凸距离的浆果范围
Vector-valued statistics of binomial processes: Berry-Esseen bounds in the convex distance
论文作者
论文摘要
我们研究了I.I.D.矢量值功能的分布之间的差异。随机元素和高斯向量的元素。我们的主要贡献是在两个分布之间的凸距离上明确绑定，并在每个维度上保持。这一发现构成了Chatterjee（2007）和Lachièze-Rey and Peccati（2017）中推论的一维界限的实质性扩展，以及在Dung（2019）和Fang and Fang和Koike（20221）中分别得出的平滑测试功能的多维测试功能和指标的多维界限。我们的技术涉及使用Stein方法的使用，并结合了Schulte和Yukich（2017）开设的递归方法的适当适应：这产生了对样本量可能具有最佳依赖性的融合速率。我们开发了几何性质的几种应用，其中包括与欧几里得空间中覆盖过程相关的内在体积的多维定量极限定理的新集合。
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 (2007) and Lachièze-Rey and Peccati (2017), as well as of the multidimensional bounds for smooth test functions and indicators of rectangles derived, respectively, in Dung (2019), and Fang and Koike (2021). Our techniques involve the use of Stein's method, combined with a suitable adaptation of the recursive approach inaugurated by Schulte and Yukich (2017): 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.
