Journal
TECHNOMETRICS
Volume 57, Issue 1, Pages 11-25Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/00401706.2013.872700
Keywords
Reduced-rank regression; Partial least squares; Principal component analysis; Canonical correlations; Sufficient dimension reduction; Grassmann manifold; Envelope model
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Funding
- National Science Foundation [DMS-1007547]
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We introduce envelopes for simultaneously reducing the predictors and the responses in multivariate linear regression, so the regression then depends only on estimated linear combinations of X and Y. We use a likelihood-based objective function for estimating envelopes and then propose algorithms for estimation of a simultaneous envelope as well as for basic Grassmann manifold optimization. The asymptotic properties of the resulting estimator are studied under normality and extended to general distributions. We also investigate likelihood ratio tests and information criteria for determining the simultaneous envelope dimensions. Simulation studies and real data examples show substantial gain over the classical methods, like partial least squares, canonical correlation analysis, and reduced-rank regression. This article has supplementary material available online.
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