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Sparse estimation of linear model via Bayesian method $$^*$$ ∗

Author

Listed:
  • Yang Yang

    (Beijing Jiaotong University)

  • Yanjiao Yang

    (Beijing Jiaotong University)

  • Lichun Wang

    (Beijing Jiaotong University)

Abstract

This paper considers the sparse estimation problem of regression coefficients in the linear model. Note that the global–local shrinkage priors do not allow the regression coefficients to be truly estimated as zero, we propose three threshold rules and compare their contraction properties, and also tandem those rules with the popular horseshoe prior and the horseshoe+ prior that are normally regarded as global–local shrinkage priors. The hierarchical prior expressions for the horseshoe prior and the horseshoe+ prior are obtained, and the full conditional posterior distributions for all parameters for algorithm implementation are also given. Simulation studies indicate that the horseshoe/horseshoe+ prior with the threshold rules are both superior to the spike-slab models. Finally, a real data analysis demonstrates the effectiveness of variable selection of the proposed method.

Suggested Citation

  • Yang Yang & Yanjiao Yang & Lichun Wang, 2024. "Sparse estimation of linear model via Bayesian method $$^*$$ ∗," Computational Statistics, Springer, vol. 39(4), pages 2011-2038, June.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:4:d:10.1007_s00180-024-01474-5
    DOI: 10.1007/s00180-024-01474-5
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    References listed on IDEAS

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    6. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
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