Multiple-Shrinkage Principal Component Regression

SUMMARY Consider the multiple-regression framework where the goal is 'black box' prediction and the explanatory variables are (approximately) multicollinear. For this situation we propose a multiple-shrinkage estimator which adaptively mimics the best principal components shrinkage estimator. The estimator proposed is a variant of the Stein estimator which is also guaranteed to give lower prediction mean-squared error than the least squares estimator, thus avoiding the danger of overshrinking when using principal components regression. The predictive performance of this estimator is illustrated and compared with that of principal components regression on three data sets by using random crossvalidation.