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Activity Number:
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313
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Type:
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Contributed
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Date/Time:
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Tuesday, August 4, 2009 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Physical and Engineering Sciences
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| Abstract - #303400 |
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Title:
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Comparison of Risks of Generalized Ridge Regression Estimators and Least Square Estimators Averaged Over the Linex Loss Function
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Author(s):
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Marvin H.J. Gruber*+
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Companies:
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Rochester Institute of Technology
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Address:
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School of Mathematical Sciences, Rochester, NY, 14623,
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Keywords:
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: asymmetric loss function ; translated ridge or least square estimator ; necessary and sufficient conditions ; over estimation and under estimation
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Abstract:
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Unlike the squared error loss function the asymmetric linex loss function takes into account the possibility of over estimation and under estimation. Necessary and sufficient conditions have been derived for the mean square error of a generalized ridge estimator to be less than that of a least square estimator. However it is virtually impossible to obtain necessary and sufficient conditions for the linex risk of a ridge estimator to be less than that of a least square estimator. It is possible to obtain sufficient conditions for the linex risk of a ridge type estimator to be less than that of a least square estimator. Sufficient conditions for the comparison of the linex risk of ridge type, least square, and related estimators will be presented.
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