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Use of Ridge and Stein-Type Estimators in Prediction

机译：岭和斯坦因型估计在预测中的应用

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For the usual regression model with fixed regressors, there is a considerable literature devoted to alternatives to ordinary least squares estimators of the regression parameters. These alternatives are biased with 'small' variances resulting in reduced mean square error over some (perhaps all) of the parameter space. Two prominent classes of such estimators are ridge type and Stein type estimators. Consider the simplest prediction problem in this context, i.e. prediction at a single new vector of prediction values. The risk (squared error) is calculated for predictors based on estimators in the above families. While the ordinary least squares predictor is admissible, a simulation study reveals that over regions of the parameter space substantial reduction in risk is possible using estimators in these families. A simple preliminary procedure based upon the vector of prediction values is given to select a good estimator from these families. It is apparent that in multiple prediction a single choice of estimator need not be best.

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