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Penalised variable selection with U-estimates

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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