TY - JOUR
T1 - The Dual Central Subspaces in dimension reduction
AU - Iaci, Ross
AU - Yin, Xiangrong
AU - ZHU, Lixing
N1 - Funding Information:
We would like to thank the Editor, Associate Editor and a referee for the careful reading of the article and the insightful comments that greatly improved the paper. Iaci’s work was supported in part by National Science Foundation grant 1309954 and Yin’s work was supported in part by National Science Foundation grant 1205546 .
PY - 2016/3/1
Y1 - 2016/3/1
N2 - Existing dimension reduction methods in multivariate analysis have focused on reducing sets of random vectors into equivalently sized dimensions, while methods in regression settings have focused mainly on decreasing the dimension of the predictor variables. However, for problems involving a multivariate response, reducing the dimension of the response vector is also desirable and important. In this paper, we develop a new concept, termed the Dual Central Subspaces (DCS), to produce a method for simultaneously reducing the dimensions of two sets of random vectors, irrespective of the labels predictor and response. Different from previous methods based on extensions of Canonical Correlation Analysis (CCA), the recovery of this subspace provides a new research direction for multivariate sufficient dimension reduction. A particular model-free approach is detailed theoretically and the performance investigated through simulation and a real data analysis.
AB - Existing dimension reduction methods in multivariate analysis have focused on reducing sets of random vectors into equivalently sized dimensions, while methods in regression settings have focused mainly on decreasing the dimension of the predictor variables. However, for problems involving a multivariate response, reducing the dimension of the response vector is also desirable and important. In this paper, we develop a new concept, termed the Dual Central Subspaces (DCS), to produce a method for simultaneously reducing the dimensions of two sets of random vectors, irrespective of the labels predictor and response. Different from previous methods based on extensions of Canonical Correlation Analysis (CCA), the recovery of this subspace provides a new research direction for multivariate sufficient dimension reduction. A particular model-free approach is detailed theoretically and the performance investigated through simulation and a real data analysis.
KW - Canonical Correlation Analysis
KW - Dimension reduction
KW - Dual Central Subspaces
KW - Multivariate analysis
KW - Visualization
UR - http://www.scopus.com/inward/record.url?scp=84954305631&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2015.12.003
DO - 10.1016/j.jmva.2015.12.003
M3 - Journal article
AN - SCOPUS:84954305631
SN - 0047-259X
VL - 145
SP - 178
EP - 189
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -