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A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty

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  • Lian, Heng

Abstract

In this short note, we demonstrate that Schwarz’s criterion, which has been used frequently in the literature on quantile regression, is consistent in variable selection. In particular, due to the recent interest in penalized likelihood for variable selection, we also show that Schwarz’s criterion consistently selects the true model combined with the SCAD-penalized estimator. Although similar results have been proved for linear regression, the results obtained here are new for quantile regression, which imposes extra technical difficulties compared to mean regression, since no closed-form solution exists.

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  • Lian, Heng, 2012. "A note on the consistency of Schwarz’s criterion in linear quantile regression with the SCAD penalty," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1224-1228.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1224-1228
    DOI: 10.1016/j.spl.2012.03.039
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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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    Cited by:

    1. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.

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