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Robust estimation and variable selection for semiparametric partially linear varying coefficient model based on modal regression

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  • Riquan Zhang
  • Weihua Zhao
  • Jicai Liu

Abstract

The semiparametric partially linear varying coefficient models (SPLVCM) are frequently used in statistical modelling, but most existing methods were built on either the least-square or likelihood-based methods, which are very sensitive to the outliers and their efficiency may be significantly reduced for heavy tail error distribution. This paper proposes a new efficient and robust estimation procedure for the SPLVCM based on modal regression. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts, and show that the estimators achieve the best convergence rate. Moreover, we develop a variable selection procedure to select significant parametric components for the SPLVCM and prove the method possessing the oracle property. We also discuss the bandwidth selection and propose an expectation-maximisation-type algorithm for the proposed estimation procedure. Some simulation results and real data analysis confirm that the newly proposed method works very competitively compared to other existing methods.

Suggested Citation

  • Riquan Zhang & Weihua Zhao & Jicai Liu, 2013. "Robust estimation and variable selection for semiparametric partially linear varying coefficient model based on modal regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 523-544, June.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:523-544
    DOI: 10.1080/10485252.2013.772179
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    Citations

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    Cited by:

    1. Wang, Kangning & Li, Shaomin, 2021. "Robust distributed modal regression for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    2. Yang, Hu & Guo, Chaohui & Lv, Jing, 2014. "A robust and efficient estimation method for single-index varying-coefficient models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 119-127.
    3. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    4. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    5. Lu Li & Kai Tan & Xuerong Meggie Wen & Zhou Yu, 2023. "Variable-dependent partial dimension reduction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 521-541, June.
    6. Yang, Hu & Yang, Jing, 2014. "A robust and efficient estimation and variable selection method for partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 227-242.
    7. 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.
    8. Wang, Kangning & Li, Shaomin & Sun, Xiaofei & Lin, Lu, 2019. "Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 257-276.
    9. Lv, Zhike & Zhu, Huiming & Yu, Keming, 2014. "Robust variable selection for nonlinear models with diverging number of parameters," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 90-97.
    10. Yunlu Jiang & Guo-Liang Tian & Yu Fei, 2019. "A robust and efficient estimation method for partially nonlinear models via a new MM algorithm," Statistical Papers, Springer, vol. 60(6), pages 2063-2085, December.
    11. Xuejun Ma & Yue Du & Jingli Wang, 2022. "Model detection and variable selection for mode varying coefficient model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 321-341, June.
    12. Zhao, Weihua & Zhang, Riquan & Liu, Jicai & Hu, Hongchang, 2015. "Robust adaptive estimation for semivarying coefficient models," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 132-141.
    13. Yang, Jing & Tian, Guoliang & Lu, Fang & Lu, Xuewen, 2020. "Single-index modal regression via outer product gradients," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    14. Qingyang Liu & Xianzheng Huang & Haiming Zhou, 2024. "The Flexible Gumbel Distribution: A New Model for Inference about the Mode," Stats, MDPI, vol. 7(1), pages 1-16, March.
    15. 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.
    16. 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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