Partial envelopes for efficient estimation in multivariate linear regression

Zhihua Su, R. Dennis Cook

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We introduce the partial envelope model, which leads to a parsimonious method for multivariate linear regression when some of the predictors are of special interest. It has the potential to achieve massive efficiency gains compared with the standard model in the estimation of the coefficients for the selected predictors. The partial envelope model is a variation on the envelope model proposed by Cook et al. (2010) but, as it focuses on part of the predictors, it has looser restrictions and can further improve the efficiency. We develop maximum likelihood estimation for the partial envelope model and discuss applications of the bootstrap. An example is provided to illustrate some of its operating characteristics.

Original languageEnglish (US)
Pages (from-to)133-146
Number of pages14
Issue number1
StatePublished - Mar 2011

Bibliographical note

Funding Information:
We are grateful to the editor and two referees for their insightful suggestion and comments that helped us improve the paper. This work was supported in part by a grant from the U.S. National Science Foundation.

Copyright 2011 Elsevier B.V., All rights reserved.


  • Dimension reduction
  • Envelope model
  • Grassmann manifold
  • Reducing subspace


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