IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v21y2009i6p683-696.html
   My bibliography  Save this article

Adaptive Lasso in high-dimensional settings

Author

Listed:
  • Zhengyan Lin
  • Yanbiao Xiang
  • Caiya Zhang

Abstract

Huang et al. [J. Huang, S. Ma, and C.-H. Zhang, Adaptive Lasso for sparse high-dimensional regression models, Statist. Sinica 18 (2008), pp. 1603–1618] have studied the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. They proved that the adaptive Lasso has an oracle property in the sense of Fan and Li [J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Am. Statist. Assoc. 96 (2001), pp. 1348–1360] and Fan and Peng [J. Fan and H. Peng, Nonconcave penalized likelihood with a diverging number of parameters, Ann. Statist. 32 (2004), pp. 928–961] under appropriate conditions. Particularly, they assumed that the errors of the linear regression model have Gaussian tails. In this paper, we relax this condition and assume that the errors have the finite 2kth moment for an integer k>0. With this assumption, we prove that the adaptive Lasso also has the oracle property under some appropriate conditions. Simulations are carried out to provide understanding of our result.

Suggested Citation

  • Zhengyan Lin & Yanbiao Xiang & Caiya Zhang, 2009. "Adaptive Lasso in high-dimensional settings," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(6), pages 683-696.
    • Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:683-696
    DOI: 10.1080/10485250902984875
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485250902984875
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485250902984875?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. 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. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    3. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    4. Emmanouil Androulakis & Christos Koukouvinos & Kalliopi Mylona & Filia Vonta, 2010. "A real survival analysis application via variable selection methods for Cox's proportional hazards model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1399-1406.
    5. Ni, Xiao & Zhang, Hao Helen & Zhang, Daowen, 2009. "Automatic model selection for partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2100-2111, October.
    6. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    7. 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.
    8. G. Aneiros & P. Vieu, 2016. "Sparse nonparametric model for regression with functional covariate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 839-859, October.
    9. Stephan Brunow & Stefanie Lösch & Ostap Okhrin, 2022. "Labor market tightness and individual wage growth: evidence from Germany," Journal for Labour Market Research, Springer;Institute for Employment Research/ Institut für Arbeitsmarkt- und Berufsforschung (IAB), vol. 56(1), pages 1-21, December.
    10. Hui Xiao & Yiguo Sun, 2020. "Forecasting the Returns of Cryptocurrency: A Model Averaging Approach," JRFM, MDPI, vol. 13(11), pages 1-15, November.
    11. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    12. Gareth M. James & Peter Radchenko & Jinchi Lv, 2009. "DASSO: connections between the Dantzig selector and lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 127-142, January.
    13. Lam, Clifford, 2008. "Estimation of large precision matrices through block penalization," LSE Research Online Documents on Economics 31543, London School of Economics and Political Science, LSE Library.
    14. Ping Wu & Xinchao Luo & Peirong Xu & Lixing Zhu, 2017. "New variable selection for linear mixed-effects models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 627-646, June.
    15. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    16. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    17. Naimoli, Antonio, 2022. "Modelling the persistence of Covid-19 positivity rate in Italy," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    18. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    19. Jian Guo & Elizaveta Levina & George Michailidis & Ji Zhu, 2010. "Pairwise Variable Selection for High-Dimensional Model-Based Clustering," Biometrics, The International Biometric Society, vol. 66(3), pages 793-804, September.
    20. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.

    More about this item

    Statistics

    Access and download statistics

    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:taf:gnstxx:v:21:y:2009:i:6:p:683-696. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.