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Semiparametric Estimation of Additive Quantile Regression Models by Two-Fold Penalty

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  • Heng Lian

Abstract

In this article, we propose a model selection and semiparametric estimation method for additive models in the context of quantile regression problems. In particular, we are interested in finding nonzero components as well as linear components in the conditional quantile function. Our approach is based on spline approximation for the components aided by two Smoothly Clipped Absolute Deviation (SCAD) penalty terms. The advantage of our approach is that one can automatically choose between general additive models, partially linear additive models, and linear models in a single estimation step. The most important contribution is that this is achieved without the need for specifying which covariates enter the linear part, solving one serious practical issue for models with partially linear additive structure. Simulation studies as well as a real dataset are used to illustrate our method.

Suggested Citation

  • Heng Lian, 2012. "Semiparametric Estimation of Additive Quantile Regression Models by Two-Fold Penalty," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 337-350, March.
  • Handle: RePEc:taf:jnlbes:v:30:y:2012:i:3:p:337-350
    DOI: 10.1080/07350015.2012.693851
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    Cited by:

    1. HONDA, Toshio & ING, Ching-Kang & WU, Wei-Ying, 2017. "Adaptively weighted group Lasso for semiparametric quantile regression models," Discussion Papers 2017-04, Graduate School of Economics, Hitotsubashi University.
    2. Xu, Qifa & Niu, Xufeng & Jiang, Cuixia & Huang, Xue, 2015. "The Phillips curve in the US: A nonlinear quantile regression approach," Economic Modelling, Elsevier, vol. 49(C), pages 186-197.
    3. repec:spr:aistmt:v:69:y:2017:i:4:d:10.1007_s10463-016-0566-9 is not listed on IDEAS
    4. repec:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0599-8 is not listed on IDEAS
    5. Zhao, Weihua & Lian, Heng, 2017. "Quantile index coefficient model with variable selection," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 40-58.
    6. Yang, Jing & Yang, Hu, 2016. "A robust penalized estimation for identification in semiparametric additive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 268-277.
    7. Lian, Heng & Meng, Jie & Fan, Zengyan, 2015. "Simultaneous estimation of linear conditional quantiles with penalized splines," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 1-21.
    8. Lian, Heng, 2015. "Quantile regression for dynamic partially linear varying coefficient time series models," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 49-66.

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