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Fitting sparse linear models under the sufficient and necessary condition for model identification

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  • Huang, Jian
  • Jiao, Yuling
  • Kang, Lican
  • Liu, Yanyan

Abstract

We propose an enhanced support detection and root finding approach (ESDAR) to variable selection in sparse linear models. ESDAR is motivated from the KKT conditions for the ℓ0 penalized regression. In ESDAR, we introduce a step size to balance the primal and dual variables in determining the support of the solution. We establish a sharp oracle error bound and an oracle support recovery property for the solution sequence generated by ESDAR under the weakest possible condition on the design matrix that is sufficient and necessary for the model to be identifiable. The conditions for the oracle results we obtained are weaker than those for Lasso and concave selection methods including SCAD and MCP in the literature.

Suggested Citation

  • Huang, Jian & Jiao, Yuling & Kang, Lican & Liu, Yanyan, 2021. "Fitting sparse linear models under the sufficient and necessary condition for model identification," Statistics & Probability Letters, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302285
    DOI: 10.1016/j.spl.2020.108925
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    References listed on IDEAS

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    1. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Aifen Feng & Jingya Fan & Zhengfen Jin & Mengmeng Zhao & Xiaogai Chang, 2023. "Research Based on High-Dimensional Fused Lasso Partially Linear Model," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    2. Li, Peili & Jiao, Yuling & Lu, Xiliang & Kang, Lican, 2022. "A data-driven line search rule for support recovery in high-dimensional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

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