Optimization of generalized Cp Criterion for Selecting Ridge Parameters in Generalized Ridge Regression

Abstract

In a generalized ridge (GR) regression, since a GR estimator (GRE) depends on ridge parameters, it is important to select those parameters appropriately. Ridge parameters selected by minimizing the generalized Cp (GCp) criterion can be obtained as closed forms. However, because the ridge parameters selected by this criterion depend on a nonnegative value α expressing the strength of the penalty for model complexity, α must be optimized for obtaining a better GRE. In this paper, we propose a method for optimizing α in the GCp criterion using [12] as similar as [7].