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
收藏
页码：1333 / 1374
页数：42
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