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Liu-type estimator in semiparametric partially linear additive models

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  • Chuanhua Wei
  • Xiaonan Wang

Abstract

Partially linear additive model is useful in statistical modelling as a multivariate nonparametric fitting technique. This paper considers statistical inference for the semiparametric model in the presence of multicollinearity. Based on the profile least-squares (PL) approach and Liu estimation method, we propose a PL Liu estimator for the parametric component. When some additional linear restrictions on the parametric component are available, the corresponding restricted Liu estimator for the parametric component is constructed. The properties of the proposed estimators are derived. Some simulations are conducted to assess the performance of the proposed procedures and the results are satisfactory. Finally, a real data example is analysed.

Suggested Citation

  • Chuanhua Wei & Xiaonan Wang, 2016. "Liu-type estimator in semiparametric partially linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 459-468, September.
    • Handle: RePEc:taf:gnstxx:v:28:y:2016:i:3:p:459-468
    DOI: 10.1080/10485252.2016.1163357
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    References listed on IDEAS

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    1. Chuan-hua Wei & Chunling Liu, 2012. "Statistical inference on semi-parametric partial linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 809-823, December.
    2. Hua Liang & Sally W. Thurston & David Ruppert & Tatiyana Apanasovich & Russ Hauser, 2008. "Additive partial linear models with measurement errors," Biometrika, Biometrika Trust, vol. 95(3), pages 667-678.
    3. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    4. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521812832.
    5. Manzan, Sebastiano & Zerom, Dawit, 2005. "Kernel estimation of a partially linear additive model," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 313-322, May.
    6. Roozbeh, M. & Arashi, M., 2013. "Feasible ridge estimator in partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 35-44.
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    Cited by:

    1. Jing Li & Xueyan Li, 2019. "Liu Estimator in Semiparametric Partially Linear Varying Coefficient Models," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-69, November.
    2. Michael Levine, 2019. "Robust functional estimation in the multivariate partial linear model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 743-770, August.

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