An unbiased Cp criterion for multivariate ridge regression

Journal of Multivariate Analysis

Volumn 101, Issue 5, 2010, Pages 1226-1238

  Yanagihara, Hirokazu ^a   Satoh, Kenichi ^b  

^a HIROSHIMA UNIVERSITY   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Bias correction; Mallows' Cp statistic; Model selection; Multivariate linear regression model; Ridge regression

Indexed keywords

EID: 77249124301     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2009.09.017     Document Type: Article

References (22)

1. Srivastava M.S. Methods of Multivariate Statistics (2002), John Wiley & Sons, New York
2. Timm N.H. Applied Multivariate Analysis (2002), Springer-Verlag, New York
3. Sârbu C., Onişor C., Posa M., Kevresan S., and Kuhajda K. Modeling and prediction (correction) of partition coefficients of bile acids and their derivatives by multivariate regression methods. Talanta 75 (2008) 651-657
4. 137Cs in freshwater fish in Finland since 1986-a statistical analysis with multivariate linear regression models. J. Environ. Radioactiv. 87 (2006) 62-76
5. Yoshimoto A., Yanagihara H., and Ninomiya Y. Finding factors affecting a forest stand growth through multivariate linear modeling. J. Jpn. For. Soc. 87 (2005) 504-512 (in Japanese)
6. Hoerl A.E., and Kennard R. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12 (1970) 55-67
7. p. Technometrics 15 (1973) 661-675
8. p. Technometrics 37 (1995) 362-372
9. p in multivariate linear regression. Biometrika 84 (1997) 707-716
10. Draper N.R., and Herzberg A.M. A ridge-regression sidelight. Amer. Statist. 41 (1987) 282-283
11. Hurvich C.M., Simonoff J.S., and Tsai C.-L. Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J. Roy. Statist. Soc. Ser. B 60 (1998) 271-293
12. p in linear regression model. Internat Statist. Rev 74 (2006) 161-168
13. p. Comm. Statist. A Theory Methods 12 (1983) 1775-1793
14. Siotani M., Hayakawa T., and Fujikoshi Y. Modern Multivariate Statistical Analysis: A Graduate Course and Handbook (1985), American Sciences Press, Columbus, Ohio
15. Efron B., and Tibshirani R.J. An Introduction to the Bootstrap (1993), Chapman & Hall/CLC, New York
16. Fujikoshi Y., Yanagihara H., and Wakaki H. Bias corrections of some criteria for selection multivariate linear regression models in a general case. Amer. J. Math. Management Sci. 25 (2005) 221-258
17. Fujikoshi Y., Noguchi T., Ohtaki M., and Yanagihara H. Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models. Ann. Inst. Statist. Math. 55 (2003) 537-553
18. Stone M. Cross-validatory choice and assessment of statistical predictions. J. Roy. Statist. Soc. Ser. B 36 (1974) 111-147
19. Craven P., and Wahba G. Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 31 (1979) 377-403
20. Brown P.J. Aspects of multivariate regression. Trabajos Investigación Oper. 31 (1980) 249-265
21. Efron B. The estimation of prediction error: covariance penalties and cross-validation. J. Amer. Statist. Assoc. 99 (2004) 619-632
22. L and generalized cross-validation in ridge regression with application to spline smoothing. Ann. Statist. 14 (1986) 1101-1112