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On the oracle property of adaptive group Lasso in high-dimensional linear models

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  • Caiya Zhang
  • Yanbiao Xiang

Abstract

In this paper, we consider the adaptive group Lasso in high-dimensional linear regression. Some extensions have been done with other fitting procedures, such as adaptive Lasso, nonconcave penalized likelihood and adaptive elastic-net. Under appropriate conditions, we establish the consistency and asymptotic normality, which means that the adaptive group Lasso shares the oracle property in high-dimensional linear regression when the number of group variables diverges with the sample size. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:1:p:249-265
    DOI: 10.1007/s00362-015-0684-0
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. A. Antoniadis & I. Gijbels & S. Lambert-Lacroix, 2014. "Penalized estimation in additive varying coefficient models using grouped regularization," Statistical Papers, Springer, vol. 55(3), pages 727-750, August.
    3. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    4. 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.
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    7. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

    1. 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.
    2. 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.
    3. Arfan Raheen Afzal & Jing Yang & Xuewen Lu, 2021. "Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters," Computational Statistics, Springer, vol. 36(2), pages 829-855, June.
    4. Behrendt, Simon & Schweikert, Karsten, 2021. "A Note on Adaptive Group Lasso for Structural Break Time Series," Econometrics and Statistics, Elsevier, vol. 17(C), pages 156-172.
    5. Yongxin Liu & Peng Zeng & Lu Lin, 2021. "Degrees of freedom for regularized regression with Huber loss and linear constraints," Statistical Papers, Springer, vol. 62(5), pages 2383-2405, October.
    6. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    7. Gabriela Ciuperca, 2019. "Adaptive group LASSO selection in quantile models," Statistical Papers, Springer, vol. 60(1), pages 173-197, February.

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