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Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models

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  • Huang, Zhensheng
  • Zhang, Riquan

Abstract

Empirical-likelihood-based inference for the nonparametric parts in semiparametric varying-coefficient partially linear (SVCPL) models is investigated. An empirical log-likelihood approach to construct the confidence regions/intervals of the nonparametric parts is developed. An estimated empirical likelihood ratio is proved to be asymptotically standard [chi]2-limit. A simulation study indicates that, compared with a normal approximation-based approach and the bootstrap method, the proposed method described herein works better in terms of coverage probabilities and average areas/widths of confidence regions/bands. An application to a real data set is illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:16:p:1798-1808
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    Cited by:

    1. 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.
    2. Zhensheng Huang, 2011. "Empirical likelihood for generalized partially linear varying-coefficient models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(6), pages 1265-1275, May.
    3. Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.
    4. Jin-Guan Lin & Yan-Yong Zhao & Hong-Xia Wang, 2015. "Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2432-2448, November.
    5. 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.
    6. Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    7. 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.
    8. Peixin Zhao & Liugen Xue, 2011. "Variable selection for varying coefficient models with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 231-245, September.
    9. Yang, Yiping & Li, Gaorong & Peng, Heng, 2014. "Empirical likelihood of varying coefficient errors-in-variables models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 1-18.
    10. 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.

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