Bounds on minimum mean squared error in ridge regression

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Abstract
The minimum MSE (mean squared error) of ridge regression coefficient estimates (for a given set of eigenvalues and variance) is a function of the transformed coefficient vector. In this paper, the authors prove that the minimum MSE is bounded, for a given coefficient vector length, by the two cases corresponding to the signal completely contained in the component associated with the smallest or largest eigenvalue. The implication for evaluating proposed estimators of the ridge regression biasing parameter is discussed.