IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v72y2020i1d10.1007_s10463-018-0692-7.html
   My bibliography  Save this article

Asymptotic theory of the adaptive Sparse Group Lasso

Author

Listed:
  • Benjamin Poignard

    (Osaka University)

Abstract

We study the asymptotic properties of a new version of the Sparse Group Lasso estimator (SGL), called adaptive SGL. This new version includes two distinct regularization parameters, one for the Lasso penalty and one for the Group Lasso penalty, and we consider the adaptive version of this regularization, where both penalties are weighted by preliminary random coefficients. The asymptotic properties are established in a general framework, where the data are dependent and the loss function is convex. We prove that this estimator satisfies the oracle property: the sparsity-based estimator recovers the true underlying sparse model and is asymptotically normally distributed. We also study its asymptotic properties in a double-asymptotic framework, where the number of parameters diverges with the sample size. We show by simulations and on real data that the adaptive SGL outperforms other oracle-like methods in terms of estimation precision and variable selection.

Suggested Citation

  • Benjamin Poignard, 2020. "Asymptotic theory of the adaptive Sparse Group Lasso," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 297-328, February.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0692-7
    DOI: 10.1007/s10463-018-0692-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-018-0692-7
    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/s10463-018-0692-7?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. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    2. 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.
    3. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    4. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, September.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    6. 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.
    7. Francq, Christian & Thieu, Le Quyen, 2019. "Qml Inference For Volatility Models With Covariates," Econometric Theory, Cambridge University Press, vol. 35(1), pages 37-72, February.
    8. Kato, Kengo, 2009. "Asymptotics for argmin processes: Convexity arguments," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1816-1829, September.
    9. Jianqing Fan, 1997. "Comments on «Wavelets in statistics: A review» by A. Antoniadis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 131-138, August.
    10. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, vol. 99(1), pages 39-61, November.
    11. 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.
    12. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    13. 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.
    14. 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. Xing Qin & Shuangge Ma & Mengyun Wu, 2023. "Two‐level Bayesian interaction analysis for survival data incorporating pathway information," Biometrics, The International Biometric Society, vol. 79(3), pages 1761-1774, September.
    2. Benjamin Poignard & Manabu Asai, 2023. "High‐dimensional sparse multivariate stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 4-22, January.
    3. Kaida Cai & Hua Shen & Xuewen Lu, 2022. "Adaptive bi-level variable selection for multivariate failure time model with a diverging number of covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 968-993, December.

    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. Massimiliano Caporin & Francesco Poli, 2017. "Building News Measures from Textual Data and an Application to Volatility Forecasting," Econometrics, MDPI, vol. 5(3), pages 1-46, August.
    2. Jiang, Liewen & Bondell, Howard D. & Wang, Huixia Judy, 2014. "Interquantile shrinkage and variable selection in quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 208-219.
    3. 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.
    4. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    5. Capanu, Marinela & Giurcanu, Mihai & Begg, Colin B. & Gönen, Mithat, 2023. "Subsampling based variable selection for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    6. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    7. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    8. Takumi Saegusa & Tianzhou Ma & Gang Li & Ying Qing Chen & Mei-Ling Ting Lee, 2020. "Variable Selection in Threshold Regression Model with Applications to HIV Drug Adherence Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 12(3), pages 376-398, December.
    9. Wentao Wang & Jiaxuan Liang & Rong Liu & Yunquan Song & Min Zhang, 2022. "A Robust Variable Selection Method for Sparse Online Regression via the Elastic Net Penalty," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    10. Zanhua Yin, 2020. "Variable selection for sparse logistic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 821-836, October.
    11. Qingliang Fan & Yaqian Wu, 2020. "Endogenous Treatment Effect Estimation with some Invalid and Irrelevant Instruments," Papers 2006.14998, arXiv.org.
    12. 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.
    13. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    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. Li Yun & O’Connor George T. & Dupuis Josée & Kolaczyk Eric, 2015. "Modeling gene-covariate interactions in sparse regression with group structure for genome-wide association studies," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(3), pages 265-277, June.
    16. Min Chen & Yimin Lian & Zhao Chen & Zhengjun Zhang, 2017. "Sure explained variability and independence screening," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 849-883, October.
    17. 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.
    18. Yanfang Zhang & Chuanhua Wei & Xiaolin Liu, 2022. "Group Logistic Regression Models with l p,q Regularization," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    19. Satre-Meloy, Aven, 2019. "Investigating structural and occupant drivers of annual residential electricity consumption using regularization in regression models," Energy, Elsevier, vol. 174(C), pages 148-168.
    20. Hidetoshi Matsui & Toshihiro Misumi, 2015. "Variable selection for varying-coefficient models with the sparse regularization," Computational Statistics, Springer, vol. 30(1), pages 43-55, 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:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0692-7. 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.