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Lasso penalized model selection criteria for high-dimensional multivariate linear regression analysis

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  • Katayama, Shota
  • Imori, Shinpei

Abstract

This paper proposes two model selection criteria for identifying relevant predictors in the high-dimensional multivariate linear regression analysis. The proposed criteria are based on a Lasso type penalized likelihood function to allow the high-dimensionality. Under the asymptotic framework that the dimension of multiple responses goes to infinity while the maximum size of candidate models has smaller order of the sample size, it is shown that the proposed criteria have the model selection consistency, that is, they can asymptotically pick out the true model. Simulation studies show that the proposed criteria outperform existing criteria when the dimension of multiple responses is large.

Suggested Citation

  • Katayama, Shota & Imori, Shinpei, 2014. "Lasso penalized model selection criteria for high-dimensional multivariate linear regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 138-150.
    • Handle: RePEc:eee:jmvana:v:132:y:2014:i:c:p:138-150
    DOI: 10.1016/j.jmva.2014.08.002
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
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    4. Yingying Fan & Cheng Yong Tang, 2013. "Tuning parameter selection in high dimensional penalized likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 531-552, June.
    5. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
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    Cited by:

    1. Piotr Pokarowski & Wojciech Rejchel & Agnieszka Sołtys & Michał Frej & Jan Mielniczuk, 2022. "Improving Lasso for model selection and prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 831-863, June.
    2. Zhao, Li & Xu, Xingzhong, 2017. "Generalized canonical correlation variables improved estimation in high dimensional seemingly unrelated regression models," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 119-126.

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