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A high-dimensional M-estimator framework for bi-level variable selection

Author

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  • Bin Luo

    (Duke University)

  • Xiaoli Gao

    (The University of North Carolina at Greensboro)

Abstract

In high-dimensional data analysis, bi-level sparsity is often assumed when covariates function group-wisely and sparsity can appear either at the group level or within certain groups. In such cases, an ideal model should be able to encourage the bi-level variable selection consistently. Bi-level variable selection has become even more challenging when data have heavy-tailed distribution or outliers exist in random errors and covariates. In this paper, we study a framework of high-dimensional M-estimation for bi-level variable selection. This framework encourages bi-level sparsity through a computationally efficient two-stage procedure. In theory, we provide sufficient conditions under which our two-stage penalized M-estimator possesses simultaneous local estimation consistency and the bi-level variable selection consistency if certain non-convex penalty functions are used at the group level. Both our simulation studies and real data analysis demonstrate satisfactory finite sample performance of the proposed estimators under different irregular settings.

Suggested Citation

  • Bin Luo & Xiaoli Gao, 2022. "A high-dimensional M-estimator framework for bi-level variable selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 559-579, June.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:3:d:10.1007_s10463-021-00809-z
    DOI: 10.1007/s10463-021-00809-z
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    References listed on IDEAS

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    1. Patrick Breheny, 2015. "The group exponential lasso for bi‐level variable selection," Biometrics, The International Biometric Society, vol. 71(3), pages 731-740, September.
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    6. Guo, Xiao & Zhang, Hai & Wang, Yao & Wu, Jiang-Lun, 2015. "Model selection and estimation in high dimensional regression models with group SCAD," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 86-92.
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    Cited by:

    1. Reetika Sarkar & Sithija Manage & Xiaoli Gao, 2024. "Stable Variable Selection for High-Dimensional Genomic Data with Strong Correlations," Annals of Data Science, Springer, vol. 11(4), pages 1139-1164, August.

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