On contractions in linear regression |
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| Affiliation: | 1. Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, and MOE Key Laboratory of System Control and Information Processing, Shanghai 200240, PR China;2. Department of Computational Mathematics, Science and Engineering and Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA |
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| Abstract: | In this paper we demonstrate how the concept of a contractive matrix plays its role in linear regression. We review some well-known facts on the outperformance of the ordinary least-squares estimator and combine these with some new results on admissibility of estimators. Moreover, results on linear sufficiency and linear completeness are given. |
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