IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v101y2014i1p57-70..html
   My bibliography  Save this article

Asymptotic properties for combined L1 and concave regularization

Author

Listed:
  • Yingying Fan
  • Jinchi Lv

Abstract

Two important goals of high-dimensional modelling are prediction and variable selection. In this article, we consider regularization with combined L1 and concave penalties, and study the sampling properties of the global optimum of the suggested method in ultrahigh-dimensional settings. The L1 penalty provides the minimum regularization needed for removing noise variables in order to achieve oracle prediction risk, while a concave penalty imposes additional regularization to control model sparsity. In the linear model setting, we prove that the global optimum of our method enjoys the same oracle inequalities as the lasso estimator and admits an explicit bound on the false sign rate, which can be asymptotically vanishing. Moreover, we establish oracle risk inequalities for the method and the sampling properties of computable solutions. Numerical studies suggest that our method yields more stable estimates than using a concave penalty alone.

Suggested Citation

  • Yingying Fan & Jinchi Lv, 2014. "Asymptotic properties for combined L1 and concave regularization," Biometrika, Biometrika Trust, vol. 101(1), pages 57-70.
  • Handle: RePEc:oup:biomet:v:101:y:2014:i:1:p:57-70.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/ast047
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. 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.
    2. Wei Lin & Jinchi Lv, 2013. "High-Dimensional Sparse Additive Hazards Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 247-264, March.
    3. 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.
    4. Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
    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. Zheng, Zemin & Li, Yang & Yu, Chongxiu & Li, Gaorong, 2018. "Balanced estimation for high-dimensional measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 78-91.
    2. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.
    3. Zhang Haixiang & Zheng Yinan & Yoon Grace & Zhang Zhou & Gao Tao & Joyce Brian & Zhang Wei & Schwartz Joel & Vokonas Pantel & Colicino Elena & Baccarelli Andrea & Hou Lifang & Liu Lei, 2017. "Regularized estimation in sparse high-dimensional multivariate regression, with application to a DNA methylation study," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(3), pages 159-171, August.

    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. 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.
    2. Bartosz Uniejewski, 2024. "Regularization for electricity price forecasting," Papers 2404.03968, arXiv.org.
    3. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2016. "The lasso for high dimensional regression with a possible change point," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 193-210, January.
    4. Qu, Lianqiang & Song, Xinyuan & Sun, Liuquan, 2018. "Identification of local sparsity and variable selection for varying coefficient additive hazards models," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 119-135.
    5. Jin, Shaobo & Moustaki, Irini & Yang-Wallentin, Fan, 2018. "Approximated penalized maximum likelihood for exploratory factor analysis: an orthogonal case," LSE Research Online Documents on Economics 88118, London School of Economics and Political Science, LSE Library.
    6. Shaobo Jin & Irini Moustaki & Fan Yang-Wallentin, 2018. "Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 628-649, September.
    7. Po-Hsien Huang & Hung Chen & Li-Jen Weng, 2017. "A Penalized Likelihood Method for Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 329-354, June.
    8. Xiang Zhang & Yichao Wu & Lan Wang & Runze Li, 2016. "Variable selection for support vector machines in moderately high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 53-76, January.
    9. Yingying Fan & Jinchi Lv, 2013. "Asymptotic Equivalence of Regularization Methods in Thresholded Parameter Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1044-1061, September.
    10. Gabriel E Hoffman & Benjamin A Logsdon & Jason G Mezey, 2013. "PUMA: A Unified Framework for Penalized Multiple Regression Analysis of GWAS Data," PLOS Computational Biology, Public Library of Science, vol. 9(6), pages 1-19, June.
    11. Zhang Haixiang & Zheng Yinan & Yoon Grace & Zhang Zhou & Gao Tao & Joyce Brian & Zhang Wei & Schwartz Joel & Vokonas Pantel & Colicino Elena & Baccarelli Andrea & Hou Lifang & Liu Lei, 2017. "Regularized estimation in sparse high-dimensional multivariate regression, with application to a DNA methylation study," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(3), pages 159-171, August.
    12. Hirose, Kei & Tateishi, Shohei & Konishi, Sadanori, 2013. "Tuning parameter selection in sparse regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 28-40.
    13. Yan, Xiaodong & Wang, Hongni & Wang, Wei & Xie, Jinhan & Ren, Yanyan & Wang, Xinjun, 2021. "Optimal model averaging forecasting in high-dimensional survival analysis," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1147-1155.
    14. Benjamin G. Stokell & Rajen D. Shah & Ryan J. Tibshirani, 2021. "Modelling high‐dimensional categorical data using nonconvex fusion penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 579-611, July.
    15. Wang, Lu & Shen, Jincheng & Thall, Peter F., 2014. "A modified adaptive Lasso for identifying interactions in the Cox model with the heredity constraint," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 126-133.
    16. He, Qianchuan & Kong, Linglong & Wang, Yanhua & Wang, Sijian & Chan, Timothy A. & Holland, Eric, 2016. "Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 222-239.
    17. 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.
    18. 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).
    19. 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.
    20. 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.

    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:oup:biomet:v:101:y:2014:i:1:p:57-70.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.