IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v108y2013i502p632-643.html
   My bibliography  Save this article

Robust Variable Selection With Exponential Squared Loss

Author

Listed:
  • Xueqin Wang
  • Yunlu Jiang
  • Mian Huang
  • Heping Zhang

Abstract

Robust variable selection procedures through penalized regression have been gaining increased attention in the literature. They can be used to perform variable selection and are expected to yield robust estimates. However, to the best of our knowledge, the robustness of those penalized regression procedures has not been well characterized. In this article, we propose a class of penalized robust regression estimators based on exponential squared loss. The motivation for this new procedure is that it enables us to characterize its robustness in a way that has not been done for the existing procedures, while its performance is near optimal and superior to some recently developed methods. Specifically, under defined regularity conditions, our estimators are -consistent and possess the oracle property. Importantly, we show that our estimators can achieve the highest asymptotic breakdown point of 1/2 and that their influence functions are bounded with respect to the outliers in either the response or the covariate domain. We performed simulation studies to compare our proposed method with some recent methods, using the oracle method as the benchmark. We consider common sources of influential points. Our simulation studies reveal that our proposed method performs similarly to the oracle method in terms of the model error and the positive selection rate even in the presence of influential points. In contrast, other existing procedures have a much lower noncausal selection rate. Furthermore, we reanalyze the Boston Housing Price Dataset and the Plasma Beta-Carotene Level Dataset that are commonly used examples for regression diagnostics of influential points. Our analysis unravels the discrepancies of using our robust method versus the other penalized regression method, underscoring the importance of developing and applying robust penalized regression methods.

Suggested Citation

  • Xueqin Wang & Yunlu Jiang & Mian Huang & Heping Zhang, 2013. "Robust Variable Selection With Exponential Squared Loss," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 632-643, June.
  • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:502:p:632-643
    DOI: 10.1080/01621459.2013.766613
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2013.766613
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2013.766613?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yunlu Jiang, 2015. "Robust estimation in partially linear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2497-2508, November.
    2. Yeşim Güney & Yetkin Tuaç & Şenay Özdemir & Olcay Arslan, 2021. "Robust estimation and variable selection in heteroscedastic regression model using least favorable distribution," Computational Statistics, Springer, vol. 36(2), pages 805-827, June.
    3. Song, Yunquan & Liang, Xijun & Zhu, Yanji & Lin, Lu, 2021. "Robust variable selection with exponential squared loss for the spatial autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    4. Guney, Yesim & Arslan, Olcay & Yavuz, Fulya Gokalp, 2022. "Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    5. Yunquan Song & Yaqi Liu & Hang Su, 2022. "Robust Variable Selection for Single-Index Varying-Coefficient Model with Missing Data in Covariates," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    6. Gijbels, I. & Vrinssen, I., 2015. "Robust nonnegative garrote variable selection in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 1-22.
    7. Liu, Jicai & Zhang, Riquan & Zhao, Weihua & Lv, Yazhao, 2013. "A robust and efficient estimation method for single index models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 226-238.
    8. Kangning Wang & Lu Lin, 2019. "Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 60(5), pages 1649-1676, October.
    9. Tianfa Xie & Ruiyuan Cao & Jiang Du, 2020. "Variable selection for spatial autoregressive models with a diverging number of parameters," Statistical Papers, Springer, vol. 61(3), pages 1125-1145, June.
    10. Qingguo Tang & R. J. Karunamuni, 2018. "Robust variable selection for finite mixture regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 489-521, June.
    11. Chai, Hao & Zhang, Qingzhao & Jiang, Yu & Wang, Guohua & Zhang, Sanguo & Ahmed, Syed Ejaz & Ma, Shuangge, 2017. "Identifying gene-environment interactions for prognosis using a robust approach," Econometrics and Statistics, Elsevier, vol. 4(C), pages 105-120.
    12. Gabriela Ciuperca, 2018. "Test by adaptive LASSO quantile method for real-time detection of a change-point," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 689-720, August.
    13. Thompson, Ryan, 2022. "Robust subset selection," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    14. Yunlu Jiang & Guo-Liang Tian & Yu Fei, 2019. "A robust and efficient estimation method for partially nonlinear models via a new MM algorithm," Statistical Papers, Springer, vol. 60(6), pages 2063-2085, December.
    15. Yang Peng & Bin Luo & Xiaoli Gao, 2022. "Robust Moderately Clipped LASSO for Simultaneous Outlier Detection and Variable Selection," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 694-707, November.
    16. Liya Fu & Zhuoran Yang & Fengjing Cai & You-Gan Wang, 2021. "Efficient and doubly-robust methods for variable selection and parameter estimation in longitudinal data analysis," Computational Statistics, Springer, vol. 36(2), pages 781-804, June.
    17. Mingqiu Wang & Guo-Liang Tian, 2016. "Robust group non-convex estimations for high-dimensional partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 49-67, March.
    18. Ping Yu & Zhongyi Zhu & Zhongzhan Zhang, 2019. "Robust exponential squared loss-based estimation in semi-functional linear regression models," Computational Statistics, Springer, vol. 34(2), pages 503-525, June.
    19. Wu, Jinran & Wang, You-Gan & Tian, Yu-Chu & Burrage, Kevin & Cao, Taoyun, 2021. "Support vector regression with asymmetric loss for optimal electric load forecasting," Energy, Elsevier, vol. 223(C).
    20. Li, Shaomin & Wang, Kangning & Ren, Yanyan, 2018. "Robust estimation and empirical likelihood inference with exponential squared loss for panel data models," Economics Letters, Elsevier, vol. 164(C), pages 19-23.
    21. Lv, Jing & Yang, Hu & Guo, Chaohui, 2015. "An efficient and robust variable selection method for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 74-88.
    22. Wentao Wang & Jiaxuan Liang & Rong Liu & Yunquan Song & Min Zhang, 2022. "A Robust Variable Selection Method for Sparse Online Regression via the Elastic Net Penalty," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    23. Elvezio Ronchetti, 2021. "The main contributions of robust statistics to statistical science and a new challenge," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 127-135, August.
    24. 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.
    25. Wang, Yibo & Karunamuni, Rohana J., 2022. "High-dimensional robust regression with Lq-loss functions," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).

    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:jnlasa:v:108:y:2013:i:502:p:632-643. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/UASA20 .

    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.