Mean square error matrix comparison of some estimators in linear regressions with multicollinearity

The ordinary least squares, the principal components regression and the ordinary ridge regression estimators are special cases of the r - k class estimator proposed by Baye and Parker (1984) for regression models with multicollinearity. We obtain necessary and sufficient conditions for the superiority of the r - k class estimator over each of these three estimators by the criterion of mean square error matrix. We also suggest tests to verify if these conditions are indeed satisfied.