TY - JOUR
T1 - Overlapped groupwise dimension reduction
AU - Zhou, Jing Ke
AU - Wu, Jian Rong
AU - ZHU, Lixing
N1 - Publisher Copyright:
© 2016, Science China Press and Springer-Verlag Berlin Heidelberg.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
KW - envelope method
KW - Gaussian graphic model
KW - groupwise dimension reduction
KW - overlapped group structure
KW - sufficient dimension reduction
UR - http://www.scopus.com/inward/record.url?scp=85000538821&partnerID=8YFLogxK
U2 - 10.1007/s11425-016-0121-5
DO - 10.1007/s11425-016-0121-5
M3 - Journal article
AN - SCOPUS:85000538821
SN - 1674-7283
VL - 59
SP - 2543
EP - 2560
JO - Science China Mathematics
JF - Science China Mathematics
IS - 12
ER -