On multivariate linear regression shrinkage and reduced-rank procedures |
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| Affiliation: | 1. INRIA and Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France;2. Sorbonne Universités, UPMC Univ Paris 06 & CNRS, UMR 7598 LJLL, Paris, F-75005, France;1. School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan;2. Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima 739-8526, Japan;1. University of Wyoming, Department of mathematics, Laramie, WY 82071-3036, United States;2. Montanuniversität Leoben, Lehrstuhl für angewandte mathematik, Peter-Tunner-Straße 25-27, 8700 Leoben, Austria;3. Bielefeld University, Fakultät für Mathematik, Universitätsstraße 25, 33615 Bielefeld, Germany;4. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Hatfield, Pretoria 0083, South Africa |
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| Abstract: | ![]()
An alternate derivation of the canonical analysis shrinkage prediction procedure of Breiman and Friedman (1997. J. Roy. Statist. Soc. B 59, 3–54) is presented for the multivariate linear model. It is based on consideration of prediction mean square error matrix, and bias of the squared sample canonical correlations. A modified procedure involving partial canonical correlation analysis is also introduced and discussed. |
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