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Estimation and inference of semi-varying coefficient models with heteroscedastic errors

Author

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  • Shen, Si-Lian
  • Cui, Jian-Ling
  • Mei, Chang-Lin
  • Wang, Chun-Wei

Abstract

This article focuses on the estimation of the parametric component, which is of primary interest, in semi-varying coefficient models with heteroscedastic errors. Specifically, we first present a procedure for estimating the variance function of the error term and the resulting estimator is proved to be consistent. Then, by applying the local linear smoothing technique, and taking the estimated error heteroscedasticity into account, we suggest a re-weighting estimation of the constant coefficients and the resulting estimators are shown to have smaller asymptotic variances than the profile least-squares estimators that neglect the error heteroscedasticity while remaining the same biases. Some simulation experiments are conducted to evaluate the finite sample performance of the proposed methodologies. Finally, a real-world data set is analyzed to demonstrate the application of the methods.

Suggested Citation

  • Shen, Si-Lian & Cui, Jian-Ling & Mei, Chang-Lin & Wang, Chun-Wei, 2014. "Estimation and inference of semi-varying coefficient models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 70-93.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:70-93
    DOI: 10.1016/j.jmva.2013.10.010
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    References listed on IDEAS

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    1. Hu, Xuemei & Wang, Zhizhong & Zhao, Zhiwei, 2009. "Empirical likelihood for semiparametric varying-coefficient partially linear errors-in-variables models," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1044-1052, April.
    2. Yang, Hu & Li, Tingting, 2010. "Empirical likelihood for semiparametric varying coefficient partially linear models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 111-121, January.
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    4. Zhao, Peixin & Xue, Liugen, 2009. "Variable selection for semiparametric varying coefficient partially linear models," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2148-2157, October.
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    6. Jinhong You & Xian Zhou, 2010. "Statistical inference on seemingly unrelated varying coefficient partially linear models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(2), pages 227-253, May.
    7. Huang, Zhensheng & Zhang, Riquan, 2009. "Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1798-1808, August.
    8. Zhang, Wenyang & Lee, Sik-Yum & Song, Xinyuan, 2002. "Local Polynomial Fitting in Semivarying Coefficient Model," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 166-188, July.
    9. You, Jinhong & Zhou, Yong, 2006. "Empirical likelihood for semiparametric varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 412-422, February.
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    Cited by:

    1. Jianhong Shi & Fanrong Zhao, 2018. "Statistical inference for heteroscedastic semi-varying coefficient EV models under restricted condition," Statistical Papers, Springer, vol. 59(2), pages 487-511, June.
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    3. Samuele Centorrino & Aman Ullah & Jing Xue, 2019. "Semiparametric Estimation of Correlated Random Coefficient Models without Instrumental Variables," Papers 1911.06857, arXiv.org.
    4. Zhao, Yan-Yong & Lin, Jin-Guan & Xu, Pei-Rong & Ye, Xu-Guo, 2015. "Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 204-221.

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