Journal
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
Volume 25, Issue 1, Pages 284-300Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/10618600.2015.1029577
Keywords
Envelopes; Reducing subspaces; Grassmann manifold
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Funding
- National Science Foundation [DMS-1007547]
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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 [GRAPHICS] -consistency of the algorithm. Supplementary materials for this article are available online.
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