Overlapped groupwise dimension reduction  

作　　者：ZHOU JingKe WU JianRong ZHU LiXing 

机构地区：[1]School of Business, Ningbo University [2]School of Mathematics and Physics, Suzhou University of Science and Technology [3]Department of Mathematics, Hong Kong Baptist University

出　　处：《Science China Mathematics》2016年第12期2543-2560,共18页中国科学：数学（英文版）

基　　金：supported by a grant from the University Grant Council of Hong Kong of China;National Natural Science Foundation of China (Grant No. 11371013);Tian Yuan Foundation for Mathematics

摘　　要：Existing groupwise dimension reduction requires given group structure to be non-overlapped. This confines its application scope. We aim at groupwise dimension reduction with overlapped group structure or even unknown group structure. To this end, existing groupwise dimension reduction concept is extended to be compatible with overlapped group structure. Then, the envelope method is ameliorated to deal with overlapped groupwise dimension reduction. As an application, Gaussian graphic model is employed to estimate the structure between predictors when the group structure is not given, and the amended envelope method is used for groupwise dimension reduction with graphic structure. Furthermore, the rationale of the proposed estimation procedure is explained at the population level and the estimation consistency is proved at the sample level. Finally, the finite sample performance of the proposed methods is examined via numerical simulations and a body fat data analysis.Existing groupwise dimension reduction requires given group structure to be non-overlapped. This confines its application scope. We aim at groupwise dimension reduction with overlapped group structure or even unknown group structure. To this end, existing groupwise dimension reduction concept is extended to be compatible with overlapped group structure. Then, the envelope method is ameliorated to deal with overlapped groupwise dimension reduction. As an application, Gaussian graphic model is employed to estimate the structure between predictors when the group structure is not given, and the amended envelope method is used for groupwise dimension reduction with graphic structure. Furthermore, the rationale of the proposed estimation procedure is explained at the population level and the estimation consistency is proved at the sample level. Finally, the finite sample performance of the proposed methods is examined via numerical simulations and a body fat data analysis.

关 键 词：sufficient dimension reduction groupwise dimension reduction overlapped group structure envelope method Gaussian graphic model 

分 类 号：O212.1[理学—概率论与数理统计]