Foundations for Envelope Models and Methods

R. Dennis Cook, Xin Zhang

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

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
Volume110
Issue number510
DOIs
StatePublished - Apr 3 2015

Keywords

  • Generalized linear models
  • Grassmannians
  • Weighted least squares

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