On the biased estimation in regression : studies on ridge-type estimation - Leskinen, Esko (1980)
In this work we have developed and studied a new ridge-type estimation method which we call the orthogonalizing ridge estimation. We have attempted to improve regression estimation with respect to the LS-estimation only in multicollinear cases. When we have the orthogonal case the orthogonalizing ridge estimation is equivalent to the LS-estimation. Further, in the orthogonalizing ridge estimation we only modify those components of the orthogonalizing ridge estimators in which the corresponding components of the LS-estimator (in the canonical form) often produce the most inaccurate estimates. When we add the orthogonalizing constant k to these components of estimators, we do not damp coefficients of estimators to zero when k increases. We have studied the MSE-properties of the orthogonalizing ridge estimators and shown that there always exists a fixed k > 0 such that their MSE's are smaller than the MSE of the LS-estimator. We have constructed a simulation study of orthogonalizing ridge estimators and ridge estimators and compared their properties with the LS-estimator and with each other. We have also applied these estimation methods to two empirical data in which the presence of multicollinearity causes serious problems in the LS-estimation.