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Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables

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  • Yang, Seong J.
  • Park, Byeong U.

Abstract

In this paper we consider partially linear varying coefficient models. We provide semiparametric efficient estimators of the parametric part as well as rate-optimal estimators of the nonparametric part. In our model, different nonparametric coefficients have different smoothing variables. This requires employing a projection technique to get proper estimators of the nonparametric coefficients, and thus conventional kernel smoothing cannot give semiparametric efficient estimators of the parametric components. We take the smooth backfitting approach in conjunction with the profiling technique to get semiparametric efficient estimators of the parametric part. We also show that our estimators of the nonparametric part achieve the univariate rate of convergence, regardless of the covariate’s dimension. We report the finite sample properties of the semiparametric efficient estimators and compare them with those of other estimators.

Suggested Citation

  • Yang, Seong J. & Park, Byeong U., 2014. "Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 100-113.
    • Handle: RePEc:eee:jmvana:v:126:y:2014:i:c:p:100-113
    DOI: 10.1016/j.jmva.2014.01.004
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    References listed on IDEAS

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    1. Yang, Lijian & Park, Byeong U. & Xue, Lan & Hardle, Wolfgang, 2006. "Estimation and Testing for Varying Coefficients in Additive Models With Marginal Integration," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1212-1227, September.
    2. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    3. 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.
    4. Xiaoke Zhang & Byeong U. Park & Jane-ling Wang, 2013. "Time-Varying Additive Models for Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 983-998, September.
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    Cited by:

    1. Fan, Guo-Liang & Liang, Han-Ying & Shen, Yu, 2016. "Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 183-201.
    2. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Rejoinder," International Statistical Review, International Statistical Institute, vol. 83(1), pages 72-76, April.

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