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Convergence and sparsity of Lasso and group Lasso in high-dimensional generalized linear models

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  • Lichun Wang
  • Yuan You
  • Heng Lian

Abstract

In this short paper, we investigate Lasso regularized generalized linear models in the “small $$n$$ n , large $$p$$ p ” setting. While similar problems have been well-studied with SCAD penalty, the study of Lasso penalty is mostly restricted to the least squares loss function. Here we show the convergence rate of the Lasso penalized estimator as well as the sparsity property under suitable assumptions. We also extend the results to group Lasso regularized models when the variables are naturally grouped. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:819-828
    DOI: 10.1007/s00362-014-0609-3
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    References listed on IDEAS

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    1. 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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    5. Michael Schomaker, 2012. "Shrinkage averaging estimation," Statistical Papers, Springer, vol. 53(4), pages 1015-1034, November.
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    Cited by:

    1. Xiaoli Gao, 2018. "A flexible shrinkage operator for fussy grouped variable selection," Statistical Papers, Springer, vol. 59(3), pages 985-1008, September.
    2. Mingrui Zhong & Zanhua Yin & Zhichao Wang, 2023. "Variable Selection for Sparse Logistic Regression with Grouped Variables," Mathematics, MDPI, vol. 11(24), pages 1-21, December.
    3. 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.
    4. 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.
    5. Gabriela Ciuperca, 2019. "Adaptive group LASSO selection in quantile models," Statistical Papers, Springer, vol. 60(1), pages 173-197, February.
    6. Chen, Yang & Luo, Ziyan & Kong, Lingchen, 2021. "ℓ2,0-norm based selection and estimation for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).

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