Statistica Sinica 28 (2018), 1179-1197
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.
Key words and phrases: Envelope models, Grassmannian, reducing subspace.