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Efficient estimation of adaptive varying-coefficient partially linear regression model

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  • Huang, Zhensheng
  • Zhang, Riquan

Abstract

The adaptive varying-coefficient partially linear regression (AVCPLR) model is proposed by combining the nonparametric regression model and varying-coefficient regression model with different smoothing variables. It can be seen as a generalization of the varying-coefficient partially linear regression model, and it is also an example of a generalized structured model as defined by Mammen and Neilsen [Mammen, E., Nielsen, J.P., 2003. Generalised structured models. Biometrika 90, 551-566]. Based on the local linear technique and the marginal integrated method, the initial estimators of these unknown functions are obtained, each of which has big variance. To decrease the variances of these initial estimators, the one-step backfitting technique proposed by Linton [Linton, O.B., 1997. Efficient estimation of additive nonparametric regression models. Biometrika 82, 93-100] is used to obtain the efficient estimators of all unknown functions for the AVCPLR model, and their asymptotic normalities are studied. Two simulated examples are given to illustrate the AVCPLR model and the proposed estimation methodology.

Suggested Citation

  • Huang, Zhensheng & Zhang, Riquan, 2009. "Efficient estimation of adaptive varying-coefficient partially linear regression model," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 943-952, April.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:7:p:943-952
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    References listed on IDEAS

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    1. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    2. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. Enno Mammen, 2003. "Generalised structured models," Biometrika, Biometrika Trust, vol. 90(3), pages 551-566, September.
    5. Zhang, Wenyang & Lee, Sik-Yum & Song, Xinyuan, 2002. "Local Polynomial Fitting in Semivarying Coefficient Model," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 166-188, July.
    6. Jens Perch Nielsen & Stefan Sperlich, 2005. "Smooth backfitting in practice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 43-61, February.
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