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A profile-type smoothed score function for a varying coefficient partially linear model


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  • Li, Gaorong
  • Feng, Sanying
  • Peng, Heng
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    The varying coefficient partially linear model is considered in this paper. When the plug-in estimators of coefficient functions are used, the resulting smoothing score function becomes biased due to the slow convergence rate of nonparametric estimations. To reduce the bias of the resulting smoothing score function, a profile-type smoothed score function is proposed to draw inferences on the parameters of interest without using the quasi-likelihood framework, the least favorable curve, a higher order kernel or under-smoothing. The resulting profile-type statistic is still asymptotically Chi-squared under some regularity conditions. The results are then used to construct confidence regions for the parameters of interest. A simulation study is carried out to assess the performance of the proposed method and to compare it with the profile least-squares method. A real dataset is analyzed for illustration.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 2 (February)
    Pages: 372-385

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:372-385

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    Keywords: Varying coefficient partially linear model Local likelihood Profile-type smoothed score function Confidence region Curse of dimensionality;


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    1. You, Jinhong & Chen, Gemai, 2006. "Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 324-341, February.
    2. Clifford Lam & Jianqing Fan, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics 31548, London School of Economics and Political Science, LSE Library.
    3. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single-index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570.
    4. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-22, July.
    5. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    6. Zhu, Lixing & Lin, Lu & Cui, Xia & Li, Gaorong, 2010. "Bias-corrected empirical likelihood in a multi-link semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 850-868, April.
    7. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    8. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    9. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    10. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    11. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    12. Qiang Chen & Lu Lin & Lixing Zhu, 2010. "Bias-corrected smoothed score function for single-index models," Metrika, Springer, vol. 71(1), pages 45-58, January.
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    Cited by:
    1. Lichun Wang & Peng Lai & Heng Lian, 2013. "Polynomial spline estimation for generalized varying coefficient partially linear models with a diverging number of components," Metrika, Springer, vol. 76(8), pages 1083-1103, November.


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