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Rank-based variable selection

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  • Brent Johnson
  • Limin Peng

Abstract

This note considers variable selection in the robust linear model via R-estimates. The proposed rank-based approach is a generalisation of the penalised least-squares estimators where we replace the least-squares loss function with Jaeckel's (1972) dispersion function. Our rank-based method is robust to outliers in the errors and has roots in traditional non-parametric statistics for simple location-shift problems. We establish the theoretical properties of our estimators which ensure desirable asymptotic behaviour of setting coefficient estimates to zero for unimportant variables and consistently estimating coefficients for important variables. Numerical studies indicate that the rank-based methods perform well for both light- and heavy-tailed error distributions.

Suggested Citation

  • Brent Johnson & Limin Peng, 2008. "Rank-based variable selection," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 241-252.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:3:p:241-252
    DOI: 10.1080/10485250801998950
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    References listed on IDEAS

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    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.
    3. Brent A. Johnson, 2008. "Variable selection in semiparametric linear regression with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 351-370, April.
    4. 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.
    5. 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.
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    Cited by:

    1. Weihua Zhao & Riquan Zhang & Yukun Liu & Jicai Liu, 2015. "Empirical likelihood based modal regression," Statistical Papers, Springer, vol. 56(2), pages 411-430, May.
    2. Asuman Turkmen & Omer Ozturk, 2014. "Rank-based ridge estimation in multiple linear regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 737-754, December.
    3. Smucler, Ezequiel & Yohai, Victor J., 2017. "Robust and sparse estimators for linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 116-130.
    4. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.
    5. Mohammad Arashi & Mina Norouzirad & S. Ejaz Ahmed & Bahadır Yüzbaşı, 2018. "Rank-based Liu regression," Computational Statistics, Springer, vol. 33(3), pages 1525-1561, September.

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