Moderate deviations for functionals over infinitely many Rademacher random variables

被引：0

作者：

Butzek, Marius ^{[1
]}

Eichelsbacher, Peter ^{[1
]}

Rednoss, Benedikt ^{[1
]}

机构：

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

来源：

ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS | 2024年 / 21卷

关键词：

Berry-Esseen bound; Cram & eacute; r-type moderate deviation; Discrete stochastic analysis; Erd & odblac; s-R & eacute; nyi random graph; Infinite weighted 2-run; Malliavin-Stein method; Rademacher functional; Subgraph count; BERRY-ESSEEN BOUNDS; NORMAL APPROXIMATION; STOCHASTIC-ANALYSIS; RANDOM GRAPHS; U-STATISTICS; THEOREMS; SUMS; CLT;

D O I：

10.30757/ALEA.v21-51

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：

In this paper, moderate deviations for normal approximation of functionals over infinitely many Rademacher random variables are derived. They are based on a bound for the Kolmogorov distance between a general Rademacher functional and a Gaussian random variable, continued by an intensive study of the behavior of operators from the Malliavin-Stein method along with the moment generating function of the mentioned functional. As applications, subgraph counting in the Erd & odblac;s-R & eacute;nyi random graph and infinite weighted 2-runs are studied.

引用

页码：1333 / 1374

页数：42