Tracking MSE efficiencies in ridge regression

Ridge regression is often favored in the analysis of ill-conditioned systems. A canonical form identifies regions in the parameter space where Ordinary Least Squares (OLS) is problematic. The objectives are two-fold: To reexamine the view that ill-conditioning necessarily degrades essentials of OLS; and to reassess ranges of the ridge parameter k where ridge is efficient in mean squared error (MSE) relative to OLS; and conversely. In particular, ridge is intended to ameliorate effects of ill-conditioning over a wide range of k. Contrary to conventional wisdom, ridge often must be abandoned in favor of OLS for k sufficiently large. 1.