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Nonconcave penalized M-estimation for the least absolute relative errors model

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  • Ruiya Fan
  • Shuguang Zhang
  • Yaohua Wu

Abstract

In this paper, we propose a nonconcave penalized M-estimation of the least absolute relative errors (penalized M-LARE) method for a sparse multiplicative regression model, where the dimension of model can increase with the sample size. Under certain appropriate conditions, the consistency and asymptotic normality for the penalized M-LARE estimator are established. Simulations and a real data analysis are in support of our theoretical results and illustrate that the proposed method performs well.

Suggested Citation

  • Ruiya Fan & Shuguang Zhang & Yaohua Wu, 2023. "Nonconcave penalized M-estimation for the least absolute relative errors model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(4), pages 1118-1135, February.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:4:p:1118-1135
    DOI: 10.1080/03610926.2021.1923749
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    Cited by:

    1. Yinjun Chen & Hao Ming & Hu Yang, 2024. "Efficient variable selection for high-dimensional multiplicative models: a novel LPRE-based approach," Statistical Papers, Springer, vol. 65(6), pages 3713-3737, August.

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