Algorithms for Envelope Estimation

R. Dennis Cook, Xin Zhang

Research output: Contribution to journalArticle

14 Scopus citations


Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable one-dimensional (1D) algorithm for estimating an envelope in general. We reveal an important structural property of envelopes that facilitates our algorithm, and we prove both Fisher consistency and (Formula presented.) -consistency of the algorithm. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)284-300
Number of pages17
JournalJournal of Computational and Graphical Statistics
Issue number1
StatePublished - Jan 2 2016


  • Envelopes
  • Grassmann manifold
  • Reducing subspaces

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