CRAMÉR-TYPE MODERATE DEVIATIONS UNDER LOCAL DEPENDENCE

被引：3

作者：

Liu, Song-hao ^{[1
]}

Zhang, Zhuo-song ^{[1
]}

机构：

[1] Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen, Peoples R China

来源：

ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 6A期

关键词：

Stein's method; Cramer-type moderate deviation; local dependence; combinatorial central limit theorem; Stein identity; NORMAL APPROXIMATION; LIMIT-THEOREMS; CRAMER; SUMS; MARTINGALES; REMAINDER; BOUNDS; RATES;

D O I：

10.1214/23-AAP1931

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 establish Cramer-type moderate deviation theorems for the sums of locally dependent random variables and combinatorial central limit theorems. Optimal error bounds and convergence ranges are obtained under some mild exponential moment conditions. Our main results are more general or sharper than the results in the literature. The main results follow from a more gen-eral Cramer-type moderate deviation theorem for dependent random variables without any boundedness assumptions, which is of independent interest. The proofs couple Stein's method with a recursive argument.

引用

页码：4747 / 4797

页数：51

共 44 条

[1]

Arras B., 2019, SpringerBriefs in Probability and Mathematical Statistics

[2] ON NORMAL APPROXIMATIONS OF DISTRIBUTIONS IN TERMS OF DEPENDENCY GRAPHS [J].

BALDI, P ;

RINOTT, Y .

ANNALS OF PROBABILITY, 1989, 17 (04) :1646-1650

[3]

Baldi P., 1989, Probability, statistics, and mathematics, P59, DOI DOI 10.1016/j.mbs.2005.03.003

[4]

BOLTHAUSEN E, 1984, Z WAHRSCHEINLICHKEIT, V66, P379, DOI 10.1007/BF00533704

[5] CERTAIN NONUNIFORM RATES OF CONVERGENCE TO NORMALITY FOR MARTINGALE DIFFERENCES [J].

BOSE, A .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1986, 14 (02) :155-167

[6]

Chatterjee S, 2014, PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL IV, P1

[7] Normal approximation under local dependence [J].

Chen, LHY ;

Shao, QM .

ANNALS OF PROBABILITY, 2004, 32 (3A) :1985-2028

[8] PALM THEORY, RANDOM MEASURES AND STEIN COUPLINGS [J].

Chen, Louis H. Y. ;

Rollin, Adrian ;

Xia, Aihua .

ANNALS OF APPLIED PROBABILITY, 2021, 31 (06) :2881-2923

[9] On the error bound in a combinatorial central limit theorem [J].

Chen, Louis H. Y. ;

Fang, Xiao .

BERNOULLI, 2015, 21 (01) :335-359

[10] FROM STEIN IDENTITIES TO MODERATE DEVIATIONS [J].

Chen, Louis H. Y. ;

Fang, Xiao ;

Shao, Qi-Man .

ANNALS OF PROBABILITY, 2013, 41 (01) :262-293

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