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Variable selection and estimation using a continuous approximation to the $$L_0$$ L 0 penalty

Author

Listed:
  • Yanxin Wang

    (Ningbo University of Technology
    University of Warwick)

  • Qibin Fan

    (Wuhan University)

  • Li Zhu

    (Xiamen University of Technology)

Abstract

Variable selection problems are typically addressed under the regularization framework. In this paper, an exponential type penalty which very closely resembles the $$L_0$$ L 0 penalty is proposed, we called it EXP penalty. The EXP penalized least squares procedure is shown to consistently select the correct model and is asymptotically normal, provided the number of variables grows slower than the number of observations. EXP is efficiently implemented using a coordinate descent algorithm. Furthermore, we propose a modified BIC tuning parameter selection method for EXP and show that it consistently identifies the correct model, while allowing the number of variables to diverge. Simulation results and data example show that the EXP procedure performs very well in a variety of settings.

Suggested Citation

  • Yanxin Wang & Qibin Fan & Li Zhu, 2018. "Variable selection and estimation using a continuous approximation to the $$L_0$$ L 0 penalty," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 191-214, February.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:1:d:10.1007_s10463-016-0588-3
    DOI: 10.1007/s10463-016-0588-3
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    References listed on IDEAS

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