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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

Abstract

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.

Suggested Citation

  • Li, Gaorong & Feng, Sanying & Peng, Heng, 2011. "A profile-type smoothed score function for a varying coefficient partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 372-385, February.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:372-385
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Jun Zhang & Bingqing Lin & Yiping Yang, 2022. "Maximum nonparametric kernel likelihood estimation for multiplicative linear regression models," Statistical Papers, Springer, vol. 63(3), pages 885-918, June.
    3. Zhang, Jun & Lin, Bingqing & Zhou, Yan, 2021. "Kernel density estimation for partial linear multivariate responses models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Sanying Feng & Liugen Xue, 2014. "Bias-corrected statistical inference for partially linear varying coefficient errors-in-variables models with restricted condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 121-140, February.
    5. Lichun Wang & Peng Lai & Heng Lian, 2013. "Polynomial spline estimation for generalized varying coefficient partially linear models with a diverging number of components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1083-1103, November.
    6. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.

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