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Consistent Bayesian information criterion based on a mixture prior for possibly high‐dimensional multivariate linear regression models

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  • Haruki Kono
  • Tatsuya Kubokawa

Abstract

In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Inheriting their asymptotic properties, our information criteria are consistent in variable selection in both the large‐sample and the high‐dimensional asymptotic frameworks. In numerical simulations, variable selection methods based on our information criteria choose the true set of variables with high probability in most cases.

Suggested Citation

  • Haruki Kono & Tatsuya Kubokawa, 2023. "Consistent Bayesian information criterion based on a mixture prior for possibly high‐dimensional multivariate linear regression models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1022-1047, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1022-1047
    DOI: 10.1111/sjos.12617
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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.
    2. Yanming Li & Bin Nan & Ji Zhu, 2015. "Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure," Biometrics, The International Biometric Society, vol. 71(2), pages 354-363, June.
    3. Hirotugu Akaike, 1980. "Seasonal Adjustment By A Bayesian Modeling," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 1-13, January.
    4. Lisha Chen & Jianhua Z. Huang, 2012. "Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1533-1545, December.
    5. 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.
    6. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    7. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    8. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2018. "A Variant of AIC Based on the Bayesian Marginal Likelihood," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 60-84, May.
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