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SCAD penalized rank regression with a diverging number of parameters

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  • Yang, Hu
  • Guo, Chaohui
  • Lv, Jing

Abstract

In this paper, we study the robust variable selection and estimation based on rank regression and SCAD penalty function in linear regression models when the number of parameters diverges with the sample size increasing. The proposed method is resistant to heavy-tailed errors or outliers in the response, since rank regression combines properties of least absolute deviation (LAD) and least squares (LS), which is generally more robust and efficient than the LS and LAD estimators, respectively. Furthermore, when the dimension pn of the predictors satisfies the condition pnlogn/n→0, as n→+∞, where n is the sample size, and the tuning parameter is chosen appropriately, the proposed estimator can identify the underlying sparse model and have desired large sample properties including n/pn consistency and asymptotic normality. Some simulation results confirm that the newly proposed method works very well compared to other existing methods.

Suggested Citation

  • Yang, Hu & Guo, Chaohui & Lv, Jing, 2015. "SCAD penalized rank regression with a diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 321-333.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:321-333
    DOI: 10.1016/j.jmva.2014.09.014
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    References listed on IDEAS

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    Cited by:

    1. Liya Fu & Zhuoran Yang & Fengjing Cai & You-Gan Wang, 2021. "Efficient and doubly-robust methods for variable selection and parameter estimation in longitudinal data analysis," Computational Statistics, Springer, vol. 36(2), pages 781-804, June.
    2. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.

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