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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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    14. 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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    16. 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.
    17. Toshio Honda, 2015. "Discussion," International Statistical Review, International Statistical Institute, vol. 83(1), pages 68-70, April.
    18. 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.
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