An unbiased CpCp criterion for multivariate ridge regression

Mallows’ CpCp statistic is widely used for selecting multivariate linear regression models. It can be considered to be an estimator of a risk function based on an expected standardized mean square error of prediction. An unbiased CpCp criterion for selecting multivariate linear regression models has been proposed. In this paper, that unbiased CpCp criterion is extended to the case of a multivariate ridge regression. It is analytically proved that the proposed criterion has not only a smaller bias but also a smaller variance than the existing CpCp criterion, and is the uniformly minimum variance unbiased estimator of the risk function. We show that the criterion has useful properties by means of numerical experiments.