An unbiased criterion for multivariate ridge regression

Mallows’ C p 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 C p criterion for selecting multivariate linear regression models has been proposed. In this paper, that unbiased C p 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 C p 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.