Dimension reduction in regression without matrix inversion

R. D Cook, Bing Li, Francesca Chiaromonte

Research output: Contribution to journalArticle

50 Scopus citations


Regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields. Sufficient dimension reduction provides a promising approach to such problems, by restricting attention to dn linear combinations of the original p predictors. However, standard methods of sufficient dimension reduction require inversion of the sample predictor covariance matrix. We propose a method for estimating the central subspace that eliminates the need for such inversion and is applicable regardless of the (n, p) relationship. Simulations show that our method compares favourably with standard large sample techniques when the latter are applicable. We illustrate our method with a genomics application.

Original languageEnglish (US)
Pages (from-to)569-584
Number of pages16
Issue number3
StatePublished - Sep 14 2007


  • Central subspace
  • Singularity of sample covariance
  • ∑-envelope

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