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Variable selection in high-dimensional quantile varying coefficient models

Author

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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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    4. 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.
    5. Chaohui Guo & Hu Yang & Jing Lv, 2017. "Robust variable selection in high-dimensional varying coefficient models based on weighted composite quantile regression," Statistical Papers, Springer, vol. 58(4), pages 1009-1033, December.
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    7. 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.
    8. 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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    14. Ciuperca, Gabriela, 2021. "Variable selection in high-dimensional linear model with possibly asymmetric errors," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    15. 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.
    16. Weihua Zhao & Jianbo Li & Heng Lian, 2018. "Adaptive varying-coefficient linear quantile model: a profiled estimating equations approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 553-582, June.
    17. Jiang, Rong & Qian, Wei-Min, 2016. "Quantile regression for single-index-coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 305-317.
    18. 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.
    19. 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.
    20. Kangning Wang, 2018. "Variable selection for spatial semivarying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 323-351, April.
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    23. 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.

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