Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

被引：16

作者：

Krokowski, Kai ^{[1
]}

Reichenbachs, Anselm ^{[1
]}

Thale, Christoph ^{[1
]}

机构：

[1] Ruhr Univ Bochum, Fac Math, Bochum, Germany

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2016年 / 52卷 / 02期

关键词：

Berry-Esseen bound; Central limit theorem; Malliavin calculus; Normal approximation; Rademacher chaos; Stein's method; GAUSSIAN FLUCTUATIONS; NORMAL APPROXIMATION; U-STATISTICS; POISSON; INVARIANCE;

D O I：

10.1214/14-AIHP652

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：

Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a connection to small ball probabilities and shed new light onto the relation between central limit theorems on the Rademacher chaos and norms of contraction operators. Applications concern infinite weighted 2-runs, a combinatorial central limit theorem and traces of Bernoulli random matrices.

引用

页码：763 / 803

页数：41

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