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Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models

Author

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  • Yunquan Song

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Zitong Li

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Minglu Fang

    (College of Science, China University of Petroleum, Qingdao 266580, China)

Abstract

The single-index model is an intuitive extension of the linear regression model. It has been increasingly popular due to its flexibility in modeling. In this work, we focus on the estimators of the parameters and the unknown link function for the single-index model in a high-dimensional situation. The SCAD and Laplace error penalty (LEP)-based penalized composite quantile regression estimators, which could realize variable selection and estimation simultaneously, are proposed; a practical iterative algorithm is introduced to obtain the efficient and robust estimators. The choices of the tuning parameters, the bandwidth, and the initial values are also discussed. Furthermore, under some mild conditions, we show the large sample properties and oracle property of the SCAD and Laplace penalized composite quantile regression estimators. Finally, we evaluated the performances of the proposed estimators by two numerical simulations and a real data application.

Suggested Citation

  • Yunquan Song & Zitong Li & Minglu Fang, 2022. "Robust Variable Selection Based on Penalized Composite Quantile Regression for High-Dimensional Single-Index Models," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2000-:d:835520
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    3. 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.
    4. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    5. 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.
    6. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    7. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    8. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    9. Canhong Wen & Xueqin Wang & Shaoli Wang, 2015. "Laplace Error Penalty-based Variable Selection in High Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 685-700, September.
    10. 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.
    11. 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. Snezhana Gocheva-Ilieva & Atanas Ivanov & Hristina Kulina, 2023. "Special Issue “Statistical Data Modeling and Machine Learning with Applications II”," Mathematics, MDPI, vol. 11(12), pages 1-4, June.
    2. Shuanghua Luo & Yuxin Yan & Cheng-yi Zhang, 2024. "Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data," Mathematics, MDPI, vol. 12(4), pages 1-15, February.
    3. Yunquan Song & Hang Su & Minmin Zhan, 2024. "Local Walsh-average-based Estimation and Variable Selection for Spatial Single-index Autoregressive Models," Networks and Spatial Economics, Springer, vol. 24(2), pages 313-339, June.

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