Sufficient dimension reduction and prediction in regression

Kofi P. Adragni, R. Dennis Cook

Research output: Contribution to journalArticle

55 Scopus citations

Abstract

Dimension reduction for regression is a prominent issue today because technological advances now allow scientists to routinely formulate regressions in which the number of predictors is considerably larger than in the past. While several methods have been proposed to deal with such regressions, principal components (PCs) still seem to be the most widely used across the applied sciences. We give a broad overview of ideas underlying a particular class of methods for dimension reduction that includes PCs, along with an introduction to the corresponding methodology. New methods are proposed for prediction in regressions with many predictors. This journal is

Original languageEnglish (US)
Pages (from-to)4385-4405
Number of pages21
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume367
Issue number1906
DOIs
StatePublished - Nov 13 2009

Keywords

  • Lasso
  • Partial least squares
  • Principal component regression
  • Principal components
  • Principal fitted components

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