Selection of Model Selection Criteria for Multivariate Ridge Regression

In the present study, we consider the selection of model selection criteria for multivariate ridge regression. There are several model selection criteria for selecting the ridge parameter in multivariate ridge regression, e.g., the Cp criterion and the modified Cp (MCp) criterion. We propose the generalized Cp (GCp) criterion, which includes Cp andMCp criteria as special cases. The GCp criterion is specified by a non-negative parameter λ, which is referred to as the penalty parameter. We attempt to select an optimal penalty parameter such that the predictive mean square error (PMSE) of the predictor of ridge regression after optimizing the ridge parameter is minimized. Through numerical experiments, we verify that the proposed optimization methods exhibit better performance than conventional optimization methods, i.e., optimizing only the ridge parameter by minimizing the Cp or MCp criterion.