Cramér-type moderate deviations under local dependence

Liu, Songhao; Zhang, Zhuosong

2023-12-01

10.1214/23-AAP1931

Annals of Applied Probability   影响因子和分区

1050-5164

We establish Cramér-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 general Cramér-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.

combinatorial central limit theorem Cramér-type moderate deviation local dependence Stein identity Stein’s method

SCI

英语

第一 ; 通讯

Hong Kong RGC GRF["14304917","14302418"] ; Singapore Ministry of Education Academic Research Fund Tier 2[MOE2018-T2-2-076]

Mathematics

Statistics & Probability

WOS:001125035500012

INST MATHEMATICAL STATISTICS-IMS

MATHEMATICS

2-s2.0-85180308222

人工提交

Southern University of Science and Technology

Liu, Songhao,Zhang, Zhuosong. Cramér-type moderate deviations under local dependence[J]. Annals of Applied Probability,2023,33(6):4747-4797.

Liu, Songhao,&Zhang, Zhuosong.(2023).Cramér-type moderate deviations under local dependence.Annals of Applied Probability,33(6),4747-4797.

Liu, Songhao,et al."Cramér-type moderate deviations under local dependence".Annals of Applied Probability 33.6(2023):4747-4797.