Dimension reduction in regression without matrix inversion

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

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
JournalBiometrika
Volume94
Issue number3
DOIs
StatePublished - Sep 14 2007

Fingerprint

Matrix Inversion
Dimension Reduction
Regression
Sufficient Dimension Reduction
Predictors
Covariance matrix
Inversion
Central Subspace
Genomics
methodology
Linear Combination
Exceed
Eliminate
Unit
Dimension reduction
genomics
sampling
Simulation
Standards

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

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Dimension reduction in regression without matrix inversion. / Cook, R. Dennis; Li, Bing; Chiaromonte, Francesca.

In: Biometrika, Vol. 94, No. 3, 14.09.2007, p. 569-584.

Research output: Contribution to journalArticle

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