NEW BERRY-ESSEEN BOUNDS FOR FUNCTIONALS OF BINOMIAL POINT PROCESSES

• 成果类型: Article
• 署名作者: Lachieze-Rey, Raphael; Peccati, Giovanni
• 署名单位: Universite Paris Cite; University of Luxembourg
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1218
• 发表日期: 2017
• 页码: 1992-2031
• 关键词: normal approximation; statistics; decompositions

摘要

We obtain explicit Berry-Esseen bounds in the Kolmogorov distance for the normal approximation of nonlinear functionals of vectors of independent random variables. Our results are based on the use of Stein's method and of random difference operators, and generalise the bounds obtained by Chatter-jee (2008), concerning normal approximations in the Wasserstein distance. In order to obtain lower bounds for variances, we also revisit the classical Hoeffding decompositions, for which we provide a new proof and a new representation. Several applications are discussed in detail: in particular, new Berry-Esseen bounds are obtained for set approximations with random tessellations, as well as for functionals of coverage processes.