NEW BERRY-ESSEEN BOUNDS FOR FUNCTIONALS OF BINOMIAL POINT PROCESSES

被引：24

作者：

Lachieze-Rey, Raphael ^{[1
]}

Peccati, Giovanni ^{[2
]}

机构：

[1] Univ Paris 05, Sorbonne Paris Cite, Lab Map5, 45 Rue St Peres, F-75006 Paris, France

[2] Univ Luxembourg, Math Res Unit, Maison Nombre 6,Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg

来源：

ANNALS OF APPLIED PROBABILITY | 2017年 / 27卷 / 04期

关键词：

Berry-Esseen bounds; binomial processes; covering processes; random tessellations; stochastic geometry; Stein's method; NORMAL APPROXIMATION; STATISTICS; DECOMPOSITIONS;

D O I：

10.1214/16-AAP1218

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1992 / 2031

页数：40

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