An unbiased Cp criterion for multivariate ridge regression

Mallows’ Cp 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. Fujikoshi and Satoh (1997) have proposed an unbiased Cp criterion (called modified Cp; MCp) for selecting multivariate linear regression models. In this paper, the unbiased Cp criterion is extended to the case of a multivariate ridge regression model. It is analytically proved that the proposed criterion has not only smaller bias but also smaller variance than an existing Cp criterion, and we show that our criterion has useful properties by means of numerical experiments. AMS 2000 subject classifications: Primary 62J07; Secondary 62F07.