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Variable selection in high-dimensional partially linear additive models for composite quantile regression

Author

Listed:
  • Guo, Jie
  • Tang, Manlai
  • Tian, Maozai
  • Zhu, Kai

Abstract

A new estimation procedure based on the composite quantile regression is proposed for the semiparametric additive partial linear models, of which the nonparametric components are approximated by polynomial splines. The proposed estimation method can simultaneously estimate both the parametric regression coefficients and nonparametric components without any specification of the error distributions. The proposed estimation method is empirically shown to be much more efficient than the popular least-squares-based estimation method for non-normal random errors, especially for Cauchy error, and almost as efficient for normal random errors. To achieve sparsity in high-dimensional and sparse additive partial linear models, of which the number of linear covariates is much larger than the sample size but that of significant covariates is small relative to the sample size, a variable selection procedure based on adaptive Lasso is proposed to conduct estimation and variable selection simultaneously. The procedure is shown to possess the oracle property, and is much superior to the adaptive Lasso penalized least-squares-based method regardless of the random error distributions. In particular, two kinds of weights in the penalty are considered, namely the composite quantile regression estimates and Lasso penalized composite quantile regression estimates. Both types of weights perform very well with the latter performing especially well in terms of precisely selecting significant variables. The simulation results are consistent with the theoretical properties. A real data example is used to illustrate the application of the proposed methods.

Suggested Citation

  • Guo, Jie & Tang, Manlai & Tian, Maozai & Zhu, Kai, 2013. "Variable selection in high-dimensional partially linear additive models for composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 56-67.
    • Handle: RePEc:eee:csdana:v:65:y:2013:i:c:p:56-67
    DOI: 10.1016/j.csda.2013.03.017
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    References listed on IDEAS

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    Cited by:

    1. Wang, Weiwei & Wu, Xianyi & Zhao, Xiaobing & Zhou, Xian, 2018. "Robust variable selection of joint frailty model for panel count data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 60-78.
    2. Hu Yang & Huilan Liu, 2016. "Penalized weighted composite quantile estimators with missing covariates," Statistical Papers, Springer, vol. 57(1), pages 69-88, March.
    3. 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.
    4. G. Aneiros & P. Vieu, 2016. "Sparse nonparametric model for regression with functional covariate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 839-859, October.
    5. Feng, Xingdong & Liu, Qiaochu & Wang, Caixing, 2023. "A lack-of-fit test for quantile regression process models," Statistics & Probability Letters, Elsevier, vol. 192(C).
    6. Boente, Graciela & Martínez, Alejandra Mercedes, 2023. "A robust spline approach in partially linear additive models," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    7. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2014. "Quantile regression and variable selection for the single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1565-1577, July.
    8. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    9. Myeonggyun Lee & Andrea B. Troxel & Mengling Liu, 2024. "Partial-linear single-index transformation models with censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 701-720, October.
    10. 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.
    11. 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.
    12. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.

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