Fast envelope algorithms

R. Dennis Cook, Xin Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we develop new fast algorithms for envelope estimation that are stable and can be used in contemporary complex envelope estimation problems. Under the sequential 1D envelope algorithm framework of Cook and Zhang (2016), we develop an envelope coordinate descent (ECD) algorithm that is shown to be much faster than the existing 1D algorithm without loss of accuracy. We also propose a novel class of envelope component screening (ECS) algorithms that serve as a screening step that can further significantly speed computation and that shows promise as precursor methodology when n = p. The ECD and ECS algorithms have both shown promising performance in extensive simulation studies and a data analysis.

Original languageEnglish (US)
Pages (from-to)1179-1197
Number of pages19
JournalStatistica Sinica
Issue number3
StatePublished - Jul 2018


  • Envelope models
  • Grassmannian
  • Reducing subspace

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