Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 1179-1197 |
| Number of pages | 19 |
| Journal | Statistica Sinica |
| Volume | 28 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 2018 |
Bibliographical note
Funding Information:The authors are grateful to the Editor, an associate editor and three referees for constructive and insightful comments that led to significant improvements in this article. Xin Zhang’s research for this article was supported in part by grants DMS-1613154 and CCF-1617691 from the National Science Foundation.
Funding Information:
The authors are grateful to the Editor, an associate editor and three referees for constructive and insightful comments that led to significant improvements in this article. Xin Zhang's research for this article was supported in part by grants DMS-1613154 and CCF-1617691 from the National Science Foundation.
Keywords
- Envelope models
- Grassmannian
- Reducing subspace