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A note on generalized ridge estimators |
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| Authors: | Jerzy K Baksalary Pawel R Pordzik Götz Trenkler |
| Institution: | 1. Department of Mathematics , Tadeusz Kotarbiński Pedagogical University , Zielona G?ra, 65069, Poland;2. Department of Mathematical and Statistical Methods , Academy of Agriculture , Poznań, 60637, Poland;3. Department of Statistics , University of Dortmund , P.O. Box 50 05 00,4600 Dortmund, Federal Republic of Germany |
| Abstract: | It is shown that a necessary and sufficient condition derived by Farebrother (1984)for a generalized ridge estimator to dominate the ordinary least-squares estimator with respect to the mean-square-error-matrix criterion in the linear regression model admits a similar interpretation as the well known criterion of Toro-Viz-carrondo and Wallace (1968)for the dominance of a restricted least-squares estimator over the ordinary least-squares estimator. Two other properties of the generalized ridge estimators, referring to the concept of admissibility, are also pointed out. |
| Keywords: | linear regression model biased estimation mean-square-error matrix generalized mean square error |