An unbiased Cp criterion for multivariate ridge regression

  • Authors:

  • Hirokazu Yanagihara;Kenichi Satoh

  • Affiliations:

  • Department of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8626, Japan;Department of Environmetrics and Biometrics, Research Institute for Radiation Biology and Medicine, Hiroshima University, 1-2-3 Kasumi, Minami-ku, Hiroshima 734-8553, Japan

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2010

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Abstract

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.