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Variable selection in high-dimensional quantile varying coefficient models

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  • Tang, Yanlin
  • Song, Xinyuan
  • Wang, Huixia Judy
  • Zhu, Zhongyi

Abstract

In this paper, we propose a two-stage variable selection procedure for high dimensional quantile varying coefficient models. The proposed method is based on basis function approximation and LASSO-type penalties. We show that the first stage penalized estimator with LASSO penalty reduces the model from ultra-high dimensional to a model that has size close to the true model, but contains the true model as a valid sub model. By applying adaptive LASSO penalty to the reduced model, the second stage excludes the remained irrelevant covariates, leading to an estimator consistent in variable selection. A simulation study and the analysis of a real data demonstrate that the proposed method performs quite well in finite samples, with regard to dimension reduction and variable selection.

Suggested Citation

  • Tang, Yanlin & Song, Xinyuan & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in high-dimensional quantile varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 115-132.
    • Handle: RePEc:eee:jmvana:v:122:y:2013:i:c:p:115-132
    DOI: 10.1016/j.jmva.2013.07.015
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    3. Hu Yang & Chaohui Guo & Jing Lv, 2016. "Variable selection for generalized varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 57(1), pages 115-132, March.
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    5. Yan-Yong Zhao & Jin-Guan Lin & Hong-Xia Wang & Xing-Fang Huang, 2017. "Jump-detection-based estimation in time-varying coefficient models and empirical applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 574-599, September.
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    10. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
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    12. Lin, Fangzheng & Tang, Yanlin & Zhu, Zhongyi, 2020. "Weighted quantile regression in varying-coefficient model with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    13. Zongwu Cai & Xiyuan Liu, 2020. "A Functional-Coefficient VAR Model for Dynamic Quantiles with Constructing Financial Network," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202017, University of Kansas, Department of Economics, revised Oct 2020.
    14. Zhao, Yan-Yong & Lin, Jin-Guan & Huang, Xing-Fang & Wang, Hong-Xia, 2016. "Adaptive jump-preserving estimates in varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 65-80.
    15. Zhao, Yan-Yong & Lin, Jin-Guan & Zhao, Jian-Qiang & Miao, Zhang-Xiao, 2022. "Estimation of semi-varying coefficient models for longitudinal data with irregular error structure," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    16. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    17. Honda, Toshio & Yabe, Ryota, 2017. "Variable selection and structure identification for varying coefficient Cox models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 103-122.
    18. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.
    19. Ciuperca, Gabriela, 2021. "Variable selection in high-dimensional linear model with possibly asymmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    20. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.
    21. Kangning Wang & Xiaofei Sun, 2020. "Efficient parameter estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data," Statistical Papers, Springer, vol. 61(3), pages 967-995, June.
    22. Zhao, Yan-Yong & Lin, Jin-Guan, 2019. "Estimation and test of jump discontinuities in varying coefficient models with empirical applications," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 145-163.
    23. Ando, Tomohiro & Li, Kunpeng & Lu, Lina, 2023. "A spatial panel quantile model with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 232(1), pages 191-213.

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