IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i1d10.1007_s00362-016-0832-1.html
   My bibliography  Save this article

Adaptive group LASSO selection in quantile models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0832-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0832-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Aguilera Morillo, María del Carmen, 2019. "Quantile regression : a penalization approach," DES - Working Papers. Statistics and Econometrics. WS 28428, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. 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.
    5. Xianwen Ding & Zhihuang Yang, 2024. "Adaptive Bi-Level Variable Selection for Quantile Regression Models with a Diverging Number of Covariates," Mathematics, MDPI, vol. 12(20), pages 1-23, October.
    6. Ciuperca, Gabriela, 2021. "Variable selection in high-dimensional linear model with possibly asymmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. 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.
    4. Karsten Schweikert, 2020. "Oracle Efficient Estimation of Structural Breaks in Cointegrating Regressions," Papers 2001.07949, arXiv.org, revised Apr 2021.
    5. 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.
    6. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    7. Dong, C. & Li, S., 2021. "Specification Lasso and an Application in Financial Markets," Cambridge Working Papers in Economics 2139, Faculty of Economics, University of Cambridge.
    8. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    9. Feng, Zhenghui & Zhu, Lixing, 2012. "An alternating determination–optimization approach for an additive multi-index model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1981-1993.
    10. Yuanyuan Shen & Katherine P. Liao & Tianxi Cai, 2015. "Sparse kernel machine regression for ordinal outcomes," Biometrics, The International Biometric Society, vol. 71(1), pages 63-70, March.
    11. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    12. Xue Wu & Chixiang Chen & Zheng Li & Lijun Zhang & Vernon M. Chinchilli & Ming Wang, 2024. "A three-stage approach to identify biomarker signatures for cancer genetic data with survival endpoints," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 863-883, July.
    13. Niko Hauzenberger & Michael Pfarrhofer & Luca Rossini, 2020. "Sparse time-varying parameter VECMs with an application to modeling electricity prices," Papers 2011.04577, arXiv.org, revised Apr 2023.
    14. Justin B. Post & Howard D. Bondell, 2013. "Factor Selection and Structural Identification in the Interaction ANOVA Model," Biometrics, The International Biometric Society, vol. 69(1), pages 70-79, March.
    15. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    16. Jonathan Boss & Alexander Rix & Yin‐Hsiu Chen & Naveen N. Narisetty & Zhenke Wu & Kelly K. Ferguson & Thomas F. McElrath & John D. Meeker & Bhramar Mukherjee, 2021. "A hierarchical integrative group least absolute shrinkage and selection operator for analyzing environmental mixtures," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    17. Muhammad Jaffri Mohd Nasir & Ramzan Nazim Khan & Gopalan Nair & Darfiana Nur, 2024. "Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model," Statistical Papers, Springer, vol. 65(5), pages 2973-3006, July.
    18. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    19. Hu, Jianhua & Liu, Xiaoqian & Liu, Xu & Xia, Ningning, 2022. "Some aspects of response variable selection and estimation in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0832-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.