标题:Limit theorems with rate of convergence under sublinear expectations
作者:Fang, Xiao; Peng, Shige; Shao, Qi-Man; Song, Yongsheng
作者机构:[Fang, Xiao; Shao, Qi-Man] Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China.; [Peng, Shige] Shandong Univ, Inst Math, Jinan 250 更多
通讯作者:Fang, X
通讯作者地址:[Fang, X]Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China.
来源:BERNOULLI
出版年:2019
卷:25
期:4A
页码:2564-2596
DOI:10.3150/18-BEJ1063
关键词:central limit theorem; G-normal distribution; law of large numbers; rate; of convergence; Stein's method; sublinear expectation
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.
收录类别:SCOPUS;SCIE;SSCI
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85072323480&doi=10.3150%2f18-BEJ1063&partnerID=40&md5=978abe67668def1875f8d28d9c4f2a84
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