Foundations for Envelope Models and Methods

R. Dennis Cook, Xin Zhang

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


Envelopes were recently proposed by Cook, Li and Chiaromonte as a method for reducing estimative and predictive variations in multivariate linear regression. We extend their formulation, proposing a general definition of an envelope and a general framework for adapting envelope methods to any estimation procedure. We apply the new envelope methods to weighted least squares, generalized linear models and Cox regression. Simulations and illustrative data analysis show the potential for envelope methods to significantly improve standard methods in linear discriminant analysis, logistic regression and Poisson regression. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)599-611
Number of pages13
JournalJournal of the American Statistical Association
Issue number510
StatePublished - Apr 3 2015

Bibliographical note

Publisher Copyright:
© 2015 American Statistical Association.


  • Generalized linear models
  • Grassmannians
  • Weighted least squares


Dive into the research topics of 'Foundations for Envelope Models and Methods'. Together they form a unique fingerprint.

Cite this