Algorithms for Envelope Estimation. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Cook, R. Dennis; Zhang, Xin
• Is Part Of: Journal of computational and graphical statistics. Volume 25:Issue 1(2016)
• Page Start: 284
• Page End: 300
• Publication Date: 2016-01-02
• Subjects: Envelopes -- Grassmann manifold -- Reducing subspaces; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2015.1029577
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract : 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 n -consistency of the algorithm. Supplementary materials for this article are available online.