Document Type

Article

Department/Program

Mathematics

Journal Title

Journal of Multivariate Analysis

Pub Date

2016

Volume

145

First Page

178

Abstract

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. (C) 2015 Elsevier Inc. All rights reserved.

DOI

10.1016/j.jmva.2015.12.003

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