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Adaptive group LASSO selection in quantile models

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  • Gabriela Ciuperca

    (Université Lyon 1, Université de Lyon)

Abstract

The paper considers a linear model with grouped explanatory variables. If the model errors are not with zero mean and bounded variance or if model contains outliers, then the least squares framework is not appropriate. Thus, the quantile regression is an interesting alternative. In order to automatically select the relevant variable groups, we propose and study here the adaptive group LASSO quantile estimator. We establish the sparsity and asymptotic normality of the proposed estimator in two cases: fixed number and divergent number of variable groups. Numerical study by Monte Carlo simulations confirms the theoretical results and illustrates the performance of the proposed estimator.

Suggested Citation

  • Gabriela Ciuperca, 2019. "Adaptive group LASSO selection in quantile models," Statistical Papers, Springer, vol. 60(1), pages 173-197, February.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0832-1
    DOI: 10.1007/s00362-016-0832-1
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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.
    2. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    3. 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.
    4. 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.
    5. Ciuperca, Gabriela, 2015. "Model selection in high-dimensional quantile regression with seamless L0 penalty," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 313-323.
    6. 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. Mohamed Ouhourane & Yi Yang & Andréa L. Benedet & Karim Oualkacha, 2022. "Group penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 495-529, September.
    2. Li, Dan & Li, Yijun & Wang, Chaoqun & Chen, Min & Wu, Qi, 2023. "Forecasting carbon prices based on real-time decomposition and causal temporal convolutional networks," Applied Energy, Elsevier, vol. 331(C).
    3. Alvaro Mendez-Civieta & M. Carmen Aguilera-Morillo & Rosa E. Lillo, 2021. "Adaptive sparse group LASSO in quantile regression," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 547-573, September.
    4. Ciuperca, Gabriela, 2021. "Variable selection in high-dimensional linear model with possibly asymmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    5. Méndez Civieta, Álvaro & Aguilera Morillo, María del Carmen & Lillo Rodríguez, Rosa Elvira, 2019. "Quantile regression : a penalization approach," DES - Working Papers. Statistics and Econometrics. WS 28428, Universidad Carlos III de Madrid. Departamento de Estadística.

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