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

Yang Yang, Yanjiao Yang and Lichun Wang ()
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Yang Yang: Beijing Jiaotong University
Yanjiao Yang: Beijing Jiaotong University
Lichun Wang: Beijing Jiaotong University

Computational Statistics, 2024, vol. 39, issue 4, No 13, 2038 pages

Abstract: 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.

Keywords: High-dimensional; Variable selection; Threshold rules; Spikeslab package (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-024-01474-5

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