The Dual Central Subspaces in dimension reduction

Ross Iaci*, Xiangrong Yin, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)178-189
Number of pages12
JournalJournal of Multivariate Analysis
Volume145
DOIs
Publication statusPublished - 1 Mar 2016

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Canonical Correlation Analysis
  • Dimension reduction
  • Dual Central Subspaces
  • Multivariate analysis
  • Visualization

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