MODERATE DEVIATIONS IN POISSON APPROXIMATION: A FIRST ATTEMPT

被引：7

作者：

Chen, Louis H. Y. ^{[1
]}

Fang, Xiao ^{[2
,3
]}

Shao, Qi-Man ^{[4
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

[2] Natl Univ Singapore, Dept Stat & Appl Probabil, Singapore 119076, Singapore

[3] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

[4] Chinese Univ Hong Kong, Dept Stat, Hong Kong, Hong Kong, Peoples R China

来源：

STATISTICA SINICA | 2013年 / 23卷 / 04期

关键词：

Local dependence; moderate deviations; Poisson approximation; size-bias coupling; Stein's method;

D O I：

10.5705/ss.2012.203s

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：

Poisson approximation using Stein's method has been extensively studied in the literature. The.main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for right-tail probabilities of sums of dependent indicators. We obtain results under certain general conditions for local dependence as well as for size-bias coupling. These results are then applied to independent indicators, 2-runs, and the matching problem.

引用

页码：1523 / 1540

页数：18

共 50 条

[41] Option pricing in the moderate deviations regime
Friz, Peter
Gerhold, Stefan
Pinter, Arpad
MATHEMATICAL FINANCE, 2018, 28 (03) : 962 - 988
[42] Moderate deviations for Markov chains with atom
Djellout, H
Guillin, A
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2001, 95 (02) : 203 - 217
[43] Moderate deviations for nonhomogeneous Markov chains
Xu, Mingzhou
Cheng, Kun
Ding, Yunzheng
STATISTICS & PROBABILITY LETTERS, 2020, 157
[44] Moderate deviations for student's statistic
Chistyakov, GP
Götze, F
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2002, 47 (03) : 415 - 428
[45] Moderate deviations for multivariate Hawkes processes
Yao, Nian
STATISTICS & PROBABILITY LETTERS, 2018, 140 : 71 - 76
[46] Moderate deviations for the maximum likelihood estimator
Gao, FQ
STATISTICS & PROBABILITY LETTERS, 2001, 55 (04) : 345 - 352
[47] Large deviations and moderate deviations for kernel density estimators of directional data
Fu Qing Gao
Li Na Li
Acta Mathematica Sinica, English Series, 2010, 26 : 937 - 950
[48] Large Deviations and Moderate Deviations for Kernel Density Estimators of Directional Data
Gao, Fu Qing
Li, Li Na
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2010, 26 (05) : 937 - 950
[49] Large Deviations and Moderate Deviations for Kernel Density Estimators of Directional Data
Fu Qing GAO School of Mathematics and Statistics
ActaMathematicaSinica(EnglishSeries), 2010, 26 (05) : 937 - 950
[50] MODERATE DEVIATIONS FOR MARTINGALES WITH BOUNDED JUMPS
Dembo, A.
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 1996, 1 : 11 - 17

← 1 2 3 4 5 →