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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Krishnamoorthy, K., Moore, B. Combining information for prediction in linear regression. Metrika 56, 73–81 (2002). https://doi.org/10.1007/s001840100159
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DOI: https://doi.org/10.1007/s001840100159