Envelopes: A new chapter in partial least squares regression

R. Dennis Cook, Liliana Forzani

Research output: Contribution to journalArticlepeer-review


We describe and elaborate on foundations that connect partial least squares regression with recently developed envelope theory and methodology. These foundations explain why PLS regression can work well in high-dimensional regressions where the number of predictors exceeds the number of observations and set it apart from other predictive methodologies. We hope that our foundational perspective will stimulate cross-fertilization between statistics and chemometrics, leading eventually to important methodological advancements.

Original languageEnglish (US)
Article numbere3287
JournalJournal of Chemometrics
Issue number10
StatePublished - Oct 1 2020


  • SIMPLS algorithm
  • abundant regressions
  • high-dimensional regressions
  • sparse regressions
  • sufficient dimension reduction

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