Limit theorems with rate of convergence under sublinear expectations

doi:10.3150/18-BEJ1063

CSpace > 应用数学研究所

	Limit theorems with rate of convergence under sublinear expectations
	Fang, Xiao 1; Peng, Shige 2; Shao, Qi-Man 1; Song, Yongsheng3
	2019-11-01
发表期刊	BERNOULLI
ISSN	1350-7265
卷号	25 期号:4A 页码:2564-2596
摘要	Under the sublinear expectation E[.] := sup(theta is an element of Theta) E-theta[.] for a given set of linear expectations {E-theta : theta is an element of Theta}, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the G-normal distribution, which was used as the limit in Peng's (Law of large numbers and central limit theorem under nonlinear expectations (2007) Preprint) central limit theorem, in a probability space.
关键词	central limit theorem G-normal distribution law of large numbers rate of convergence Stein's method sublinear expectation
DOI	10.3150/18-BEJ1063
语种	英语
资助项目	CUHK ; NSF[11626247] ; Hong Kong RGC[GRF 14302515] ; Hong Kong RGC[14304917] ; NCMIS, NSFC[11688101] ; Key Research Program of Frontier Sciences, CAS[QYZDB-SSW-SYS017]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000485825100006
出版者	INT STATISTICAL INST
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35629
专题	应用数学研究所
通讯作者	Fang, Xiao
作者单位	1.Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China 2.Shandong Univ, Inst Math, Jinan 250100, Shandong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Fang, Xiao,Peng, Shige,Shao, Qi-Man,et al. Limit theorems with rate of convergence under sublinear expectations[J]. BERNOULLI,2019,25(4A):2564-2596.
APA	Fang, Xiao,Peng, Shige,Shao, Qi-Man,&Song, Yongsheng.(2019).Limit theorems with rate of convergence under sublinear expectations.BERNOULLI,25(4A),2564-2596.
MLA	Fang, Xiao,et al."Limit theorems with rate of convergence under sublinear expectations".BERNOULLI 25.4A(2019):2564-2596.