The Dual Central Subspaces in dimension reduction

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• 作者：Ross Iaci^a ; ^{riaci@wm.edu" class="auth_mail" title="E-mail the corresponding author} ; Xiangrong Yin^b ; ^{yinxiangrong@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Lixing Zhu^c ; ^{lzhu@hkbu.hk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62H20 ; 62H12 ; 62G07 ; 62B10
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：145
• 期：Complete
• 页码：178-189
• 全文大小：474 K

文摘

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.