Dimension reduction via an alternating inverse regression

Li Ping Zhu*, Xiangrong Yin, Lixing ZHU

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


In this article, we propose an alternating inverse regression (AIR) to estimate the central subspace (CS) in a successive manner. Taking advantage of both sliced inverse regression (SIR) and partial least squares (PLS), AIR circumvents the collinearity and curse of dimensionality simultaneously. A modified BIC criterion with a penalty term achieving an optimal convergence rate is suggested to estimate the dimension of the CS. We also extend AIR to the multivariate responses case. Through illustrative examples and a real dataset, we demonstrate the usefulness of AIR, and its advantages over some existing methods. Supplemental materials for this article are available online.

Original languageEnglish
Pages (from-to)887-899
Number of pages13
JournalJournal of Computational and Graphical Statistics
Issue number4
Publication statusPublished - Dec 2010

Scopus Subject Areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Central subspace
  • Dimension reduction subspace
  • Partial least squares
  • Sliced inverse regression


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