Combining information for prediction in linear regression |
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Authors: | Krishnamoorthy K Moore Brett C |
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Institution: | (1) Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, U.S.A. (e-mail: krishna@louisiana.edu), US;(2) Service Sector Statistics Division, Census Bureau, Mailstop 6500, Room 2754-3, Washington, DC 20233, US |
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Abstract: | This article deals with the prediction problem in linear regression where the measurements are obtained using k different devices or collected from k different independent sources. For the case of k=2, a Graybill-Deal type combined estimtor for the regression parameters is shown to dominate the individual least squares
estimators under the covariance criterion. Two predictors ŷ
c and ŷ
p are proposed. ŷ
c is based on a combined estimator of the regression coefficient vector, and ŷ
p is obtained by combining the individual predictors from different models. Prediction mean square errors of both predictors
are derived. It is shown that the predictor ŷ
p is better than the individual predictors for k≥2 and the predictor ŷ
c is better than the individual predictors for k=2. Numerical comparison between ŷ
c and ŷ
p shows that the former is superior to the latter for the case k=2. |
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Keywords: | : Covariance Criterion Graybill-Deal Estimator MINQUE Prediction Mean Square Error |
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