Combining information for prediction in linear regression

This article deals with the prediction problem in linear regression where the measurements are obtained using k di¤erent devices or collected from k di¤erent independent sources. For the case of k 1⁄4 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 ŷc and ŷp are proposed. ŷc is based on a combined estimator of the regression coe‰cient vector, and ŷp is obtained by combining the individual predictors from di¤erent models. Prediction mean square errors of both predictors are derived. It is shown that the predictor ŷp is better than the individual predictors for kb 2 and the predictor ŷc is better than the individual predictors for k 1⁄4 2. Numerical comparison between ŷc and ŷp shows that the former is superior to the latter for the case k 1⁄4 2.