Inner envelopes: Efficient estimation in multivariate linear regression

Zhihua Su, R. Dennis Cook

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

In this article we propose a new model, called the inner envelope model, which leads to efficient estimation in the context of multivariate normal linear regression. The asymptotic distribution and the consistency of its maximum likelihood estimators are established. Theoretical results, simulation studies and examples all show that the efficiency gains can be substantial relative to standard methods and to the maximum likelihood estimators from the envelope model introduced recently by Cook et al. (2010). Compared to the envelope model, the inner envelope model is based on a different construction and it can produce substantial efficiency gains in situations where the envelope model offers no gains. In effect, inner envelopes open a new frontier to the way in which reducing subspaces can be used to improve efficiency in multivariate problems.

Original languageEnglish (US)
Pages (from-to)687-702
Number of pages16
JournalBiometrika
Volume99
Issue number3
DOIs
StatePublished - Sep 2012

Bibliographical note

Funding Information:
We are grateful to the editor and two referees for their insightful suggestions and comments that helped us improve the paper. The wine data were obtained from http://www.ailab. si/orange/datasets.psp. Research for this article was supported in part by a grant from the U.S. National Science Foundation.

Keywords

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

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