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New Robust Variable Selection Methods for Linear Regression Models

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  • Ziqi Chen
  • Man-Lai Tang
  • Wei Gao
  • Ning-Zhong Shi

Abstract

type="main" xml:id="sjos12057-abs-0001"> Motivated by an entropy inequality, we propose for the first time a penalized profile likelihood method for simultaneously selecting significant variables and estimating unknown coefficients in multiple linear regression models in this article. The new method is robust to outliers or errors with heavy tails and works well even for error with infinite variance. Our proposed approach outperforms the adaptive lasso in both theory and practice. It is observed from the simulation studies that (i) the new approach possesses higher probability of correctly selecting the exact model than the least absolute deviation lasso and the adaptively penalized composite quantile regression approach and (ii) exact model selection via our proposed approach is robust regardless of the error distribution. An application to a real dataset is also provided.

Suggested Citation

  • Ziqi Chen & Man-Lai Tang & Wei Gao & Ning-Zhong Shi, 2014. "New Robust Variable Selection Methods for Linear Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 725-741, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:725-741
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    File URL: http://hdl.handle.net/10.1111/sjos.12057
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    References listed on IDEAS

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    Cited by:

    1. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    2. Ziqi Chen & Jing Ning & Yu Shen & Jing Qin, 2021. "Combining primary cohort data with external aggregate information without assuming comparability," Biometrics, The International Biometric Society, vol. 77(3), pages 1024-1036, September.
    3. Ziqi Chen & Man†Lai Tang & Wei Gao, 2018. "A profile likelihood approach for longitudinal data analysis," Biometrics, The International Biometric Society, vol. 74(1), pages 220-228, March.
    4. Florian Frommlet & Grégory Nuel, 2016. "An Adaptive Ridge Procedure for L0 Regularization," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-23, February.

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