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Variable selection for semiparametric varying coefficient partially linear errors-in-variables models

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  • Zhao, Peixin
  • Xue, Liugen

Abstract

This paper focuses on the variable selections for semiparametric varying coefficient partially linear models when the covariates in the parametric and nonparametric components are all measured with errors. A bias-corrected variable selection procedure is proposed by combining basis function approximations with shrinkage estimations. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the regularized estimators are established. A simulation study and a real data application are undertaken to evaluate the finite sample performance of the proposed method.

Suggested Citation

  • Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1872-1883
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    Cited by:

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    2. Zhihua Sun & Dongshan Luo & Xiaohua Zhou & Qingzhao Zhang, 2021. "Comparative studies on the adequacy check of parametric measurement error models with auxiliary variable," Statistical Papers, Springer, vol. 62(4), pages 1723-1751, August.
    3. Xing-cai Zhou & Jin-Guan Lin, 2014. "Empirical likelihood for varying-coefficient semiparametric mixed-effects errors-in-variables models with longitudinal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 51-69, March.
    4. Liu-Cang Wu & Zhong-Zhan Zhang & Deng-Ke Xu, 2012. "Variable selection in joint mean and variance models of Box--Cox transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(12), pages 2543-2555, August.
    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.
    6. Tian, Ruiqin & Xue, Liugen & Xu, Dengke, 2016. "Automatic variable selection for varying coefficient models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 84-90.
    7. Yang, Seong J. & Park, Byeong U., 2014. "Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 100-113.
    8. Tian, Ruiqin & Xue, Liugen & Liu, Chunling, 2014. "Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 94-110.
    9. Weiming Yang & Yiping Yang, 2020. "Composite quantile regression estimation of linear error-in-variable models using instrumental variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 1-16, January.
    10. Zhimeng Sun & Zhi Su & Jingyi Ma, 2014. "Focused vector information criterion model selection and model averaging regression with missing response," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 415-432, April.
    11. Xu, Dengke & Zhang, Zhongzhan, 2013. "A semiparametric Bayesian approach to joint mean and variance models," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1624-1631.
    12. 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.
    13. Arfan Raheen Afzal & Jing Yang & Xuewen Lu, 2021. "Variable selection in partially linear additive hazards model with grouped covariates and a diverging number of parameters," Computational Statistics, Springer, vol. 36(2), pages 829-855, June.
    14. Feng, Sanying & Xue, Liugen, 2015. "Model detection and estimation for single-index varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 227-244.
    15. Jie Zeng & Weihu Cheng & Guozhi Hu, 2023. "Optimal Model Averaging Estimation for the Varying-Coefficient Partially Linear Models with Missing Responses," Mathematics, MDPI, vol. 11(8), pages 1-21, April.
    16. Cai, Zongwu & Juhl, Ted & Yang, Bingduo, 2015. "Functional index coefficient models with variable selection," Journal of Econometrics, Elsevier, vol. 189(2), pages 272-284.
    17. Ping Yu & Jiang Du & Zhongzhan Zhang, 2020. "Single-index partially functional linear regression model," Statistical Papers, Springer, vol. 61(3), pages 1107-1123, June.
    18. Liucang Wu & Huiqiong Li, 2012. "Variable selection for joint mean and dispersion models of the inverse Gaussian distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 795-808, August.
    19. Sanying Feng & Liugen Xue, 2013. "Variable selection for partially varying coefficient single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2637-2652, December.
    20. Mingqiu Wang & Peixin Zhao & Xiaoning Kang, 2020. "Structure identification for varying coefficient models with measurement errors based on kernel smoothing," Statistical Papers, Springer, vol. 61(5), pages 1841-1857, October.
    21. Xiao-Feng Wang & Bo Hu & Bin Wang & Kuangnan Fang, 2014. "Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1342-1357, June.

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