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 (Formula presented.) -consistency of the algorithm. Supplementary materials for this article are available online.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 284-300 |
| Number of pages | 17 |
| Journal | Journal of Computational and Graphical Statistics |
| Volume | 25 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2 2016 |
Bibliographical note
Publisher Copyright:© 2016 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
Keywords
- Envelopes
- Grassmann manifold
- Reducing subspaces
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