Tensor Bernstein concentration inequalities with an application to sample estimators for high-order moments  

作　　者：Ziyan LUO Liqun QI Philippe LTOINT 

机构地区：[1]Department of Applied Mathematics,School of Science,Beijing Jiaotong University,Beijing 100044,China [2]Department of Mathematics,School of Science,Hangzhou Dianzi University,Hangzhou 310018,China [3]Department of Applied Mathematics,The Hong Kong Polytechnic University,Hung Horn,Kowloon,Hong Kong,China [4]Namur Center for Complex Systems(naXys),University of Namur,61,rue de Bruxelles,B-5000 Namur,Belgium

出　　处：《Frontiers of Mathematics in China》2020年第2期367-384,共18页中国高等学校学术文摘·数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11771038);the Beijing Natural Science Foundation(Grant No.Z190002);the Hong Kong Research Grant Council(Grant Nos.PolyU 15300715,15301716,15300717)。

摘　　要：This paper develops the Bernstein tensor concentration inequality for random tensors of general order,based on the use of Einstein products for tensors.This establishes a strong link between these and matrices,which in turn allows exploitation of existing results for the latter.An interesting application to sample estimators of high-order moments is presented as an illustration.

关 键 词：Random tensors concentration inequality Einstein products SUBSAMPLING computational statistics 

分 类 号：O183[理学—数学]