IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v22y2010i4p499-515.html
   My bibliography  Save this article

Penalised variable selection with U-estimates

Author

Listed:
  • Xiao Song
  • Shuangge Ma

Abstract

U-estimates are defined as maximisers of objective functions that are U-statistics. As an alternative to M-estimates, U-estimates have been extensively used in linear regression, classification, survival analysis, and many other areas. They may rely on weaker data and model assumptions and be preferred over alternatives. In this article, we investigate penalised variable selection with U-estimates. We propose smooth approximations of the objective functions, which can greatly reduce computational cost without affecting asymptotic properties. We study penalised variable selection using penalties that have been well investigated with M-estimates, including the LASSO, adaptive LASSO, and bridge, and establish their asymptotic properties. Generically applicable computational algorithms are described. Performance of the penalised U-estimates is assessed using numerical studies.

Suggested Citation

  • Xiao Song & Shuangge Ma, 2010. "Penalised variable selection with U-estimates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 499-515.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:499-515
    DOI: 10.1080/10485250903348781
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485250903348781
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485250903348781?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. Shuangge Ma & Jian Huang, 2007. "Combining Multiple Markers for Classification Using ROC," Biometrics, The International Biometric Society, vol. 63(3), pages 751-757, September.
    3. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    4. Jian Huang & Shuangge Ma & Huiliang Xie, 2006. "Regularized Estimation in the Accelerated Failure Time Model with High-Dimensional Covariates," Biometrics, The International Biometric Society, vol. 62(3), pages 813-820, September.
    5. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    6. Khan, Shakeeb & Tamer, Elie, 2007. "Partial rank estimation of duration models with general forms of censoring," Journal of Econometrics, Elsevier, vol. 136(1), pages 251-280, January.
    7. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
    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. Liang, Weijuan & Ma, Shuangge & Lin, Cunjie, 2021. "Marginal false discovery rate for a penalized transformation survival model," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    2. Shi, Xingjie & Huang, Yuan & Huang, Jian & Ma, Shuangge, 2018. "A Forward and Backward Stagewise algorithm for nonconvex loss functions with adaptive Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 235-251.

    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. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2017. "Correction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 883-883, April.
    2. Chen, Songnian, 2010. "Root-N-consistent estimation of fixed-effect panel data transformation models with censoring," Journal of Econometrics, Elsevier, vol. 159(1), pages 222-234, November.
    3. Patrick Bajari & Jeremy Fox & Stephen Ryan, 2008. "Evaluating wireless carrier consolidation using semiparametric demand estimation," Quantitative Marketing and Economics (QME), Springer, vol. 6(4), pages 299-338, December.
    4. repec:hal:wpspec:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    5. Shakeeb Khan & Arnaud Maurel & Yichong Zhang, 2019. "Informational Content of Factor Structures in Simultaneous Binary Response Models," Boston College Working Papers in Economics 985, Boston College Department of Economics.
    6. Youngki Shin & Zvezdomir Todorov, 2021. "Exact computation of maximum rank correlation estimator," The Econometrics Journal, Royal Economic Society, vol. 24(3), pages 589-607.
    7. Coppejans, Mark, 2001. "Estimation of the binary response model using a mixture of distributions estimator (MOD)," Journal of Econometrics, Elsevier, vol. 102(2), pages 231-269, June.
    8. Subbotin, Viktor, 2007. "Asymptotic and bootstrap properties of rank regressions," MPRA Paper 9030, University Library of Munich, Germany, revised 20 Mar 2008.
    9. Jochmans, Koen, 2015. "Multiplicative-error models with sample selection," Journal of Econometrics, Elsevier, vol. 184(2), pages 315-327.
    10. repec:hal:spmain:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    11. David E. Card & David S. Lee & Zhuan Pei & Andrea Weber, 2012. "Nonlinear Policy Rules and the Identification and Estimation of Causal Effects in a Generalized Regression Kink Design," NRN working papers 2012-14, The Austrian Center for Labor Economics and the Analysis of the Welfare State, Johannes Kepler University Linz, Austria.
    12. Shakeeb Khan & Arnaud Maurel & Yichong Zhang, 2023. "Informational Content of Factor Structures in Simultaneous Binary Response Models," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 385-410, Emerald Group Publishing Limited.
    13. Chen, Songnian, 2000. "Efficient estimation of binary choice models under symmetry," Journal of Econometrics, Elsevier, vol. 96(1), pages 183-199, May.
    14. Bijwaard Govert E. & Ridder Geert & Woutersen Tiemen, 2013. "A Simple GMM Estimator for the Semiparametric Mixed Proportional Hazard Model," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 1-23, July.
    15. Yanqin Fan & Fang Han & Wei Li & Xiao-Hua Zhou, 2019. "On rank estimators in increasing dimensions," Papers 1908.05255, arXiv.org.
    16. Horowitz, Joel L., 2002. "Bootstrap critical values for tests based on the smoothed maximum score estimator," Journal of Econometrics, Elsevier, vol. 111(2), pages 141-167, December.
    17. Fan, Yanqin & Han, Fang & Li, Wei & Zhou, Xiao-Hua, 2020. "On rank estimators in increasing dimensions," Journal of Econometrics, Elsevier, vol. 214(2), pages 379-412.
    18. Chen, Songnian & Zhou, Yahong, 2007. "Estimating a generalized correlation coefficient for a generalized bivariate probit model," Journal of Econometrics, Elsevier, vol. 141(2), pages 1100-1114, December.
    19. Yan, Jin & Yoo, Hong Il, 2019. "Semiparametric estimation of the random utility model with rank-ordered choice data," Journal of Econometrics, Elsevier, vol. 211(2), pages 414-438.
    20. Lin, Huazhen & Li, Yi & Tan, Ming T., 2013. "Estimating a unitary effect summary based on combined survival and quantitative outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 129-139.
    21. Hung Hung & Chin‐Tsang Chiang, 2010. "Optimal Composite Markers for Time‐Dependent Receiver Operating Characteristic Curves with Censored Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 664-679, December.
    22. Frederiksen, Anders & Honore, Bo E. & Hu, Luojia, 2007. "Discrete time duration models with group-level heterogeneity," Journal of Econometrics, Elsevier, vol. 141(2), pages 1014-1043, December.

    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:22:y:2010:i:4:p:499-515. 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.