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Adaptive group Lasso for high-dimensional generalized linear models

Author

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  • Mingqiu Wang

    (Qufu Normal University)

  • Guo-Liang Tian

    (Southern University of Science and Technology)

Abstract

Variable selection in a grouped manner is an attractive method since it respects the grouping structure in the data. In this paper, we study the adaptive group Lasso in the frame of high-dimensional generalized linear models. Both the number of groups diverging with the sample size and the number of groups exceeding the sample size are considered. The selection consistency and asymptotic normality of the adaptive group Lasso are established under appropriate conditions. Simulation studies confirm superior performances of the adaptive group Lasso.

Suggested Citation

  • Mingqiu Wang & Guo-Liang Tian, 2019. "Adaptive group Lasso for high-dimensional generalized linear models," Statistical Papers, Springer, vol. 60(5), pages 1469-1486, October.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0882-z
    DOI: 10.1007/s00362-017-0882-z
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    References listed on IDEAS

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    1. Lichun Wang & Yuan You & Heng Lian, 2015. "Convergence and sparsity of Lasso and group Lasso in high-dimensional generalized linear models," Statistical Papers, Springer, vol. 56(3), pages 819-828, August.
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    3. Jian Huang & Shuange Ma & Huiliang Xie & Cun-Hui Zhang, 2009. "A group bridge approach for variable selection," Biometrika, Biometrika Trust, vol. 96(2), pages 339-355.
    4. Ming Yuan & Yi Lin, 2007. "On the non‐negative garrotte estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 143-161, April.
    5. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    6. Caiya Zhang & Yanbiao Xiang, 2016. "On the oracle property of adaptive group Lasso in high-dimensional linear models," Statistical Papers, Springer, vol. 57(1), pages 249-265, March.
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    Cited by:

    1. Kristoffer Pons Bertelsen, 2022. "The Prior Adaptive Group Lasso and the Factor Zoo," CREATES Research Papers 2022-05, Department of Economics and Business Economics, Aarhus University.

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