An unbiased Cp criterion for multivariate ridge regression

JOURNAL OF MULTIVARIATE ANALYSIS

卷:101

Article

Yanagihara, Hirokazu¹  Satoh, Kenichi² 

[1] Hiroshima Univ, Grad Sch Sci, Dept Math, Hiroshima 7398626, Japan

[2] Hiroshima Univ, Res Inst Radiat Biol & Med, Dept Environmetr & Biometr, Minami Ku, Hiroshima 7348553, Japan

关键词: Bias correction;    Mallows' C-p statistic;    Model selection;    Multivariate linear regression model;    Ridge regression;   

DOI  :  10.1016/j.jmva.2009.09.017

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free