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Generalized ridge estimator and model selection criteria in multivariate linear regression

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  • Mori, Yuichi
  • Suzuki, Taiji

Abstract

We propose new model selection criteria based on generalized ridge estimators dominating the maximum likelihood estimator under the squared risk and the Kullback–Leibler risk in multivariate linear regression. Our model selection criteria have the following desirable properties: consistency, unbiasedness, and uniformly minimum variance. Consistency is proven under an asymptotic structure p∕n→c, where n is the sample size and p is the parameter dimension of the response variables. In particular, our proposed class of estimators dominates the maximum likelihood estimator under the squared risk, even when the model does not include the true model. Experimental results show that the risks of our model selection criteria are smaller than those based on the maximum likelihood estimator, and that our proposed criteria specify the true model under some conditions.

Suggested Citation

  • Mori, Yuichi & Suzuki, Taiji, 2018. "Generalized ridge estimator and model selection criteria in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 243-261.
    • Handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:243-261
    DOI: 10.1016/j.jmva.2017.12.006
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    References listed on IDEAS

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    1. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    2. Fujikoshi, Yasunori & Sakurai, Tetsuro & Yanagihara, Hirokazu, 2014. "Consistency of high-dimensional AIC-type and Cp-type criteria in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 184-200.
    3. Konno, Yoshihiko, 1991. "On estimation of a matrix of normal means with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 44-55, January.
    4. Yanagihara, Hirokazu & Satoh, Kenichi, 2010. "An unbiased Cp criterion for multivariate ridge regression," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1226-1238, May.
    5. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    6. Tsukuma, Hisayuki, 2009. "Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2296-2304, November.
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