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Estimation in generalised varying-coefficient models with unspecified link functions

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  • Zhang, Wenyang
  • Li, Degui
  • Xia, Yingcun

Abstract

In this paper, we study the generalised varying-coefficient models, where the link function is unspecified and the response variable can be either continuous or discrete. As the link function is unspecified, the models under investigation become unidentifiable. In this paper, we derive an identification condition for the generalised varying-coefficient models, which is much weaker and more reasonable than that given by Kuruwita et al. (2011) whose model can be seen as a special case of our modelling framework. Under the identification condition, we introduce a nonparametric iterative procedure to estimate the functional coefficient with its direction and norm as well as the unspecified link function, and then establish the asymptotic properties of the resulting nonparametric estimators. Furthermore, a weighted least squares based algorithm is provided to implement the iterative estimation procedure. The simulation studies and empirical application show that our estimation methodology works quite well in both small and median sample cases.

Suggested Citation

  • Zhang, Wenyang & Li, Degui & Xia, Yingcun, 2015. "Estimation in generalised varying-coefficient models with unspecified link functions," Journal of Econometrics, Elsevier, vol. 187(1), pages 238-255.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:1:p:238-255
    DOI: 10.1016/j.jeconom.2015.02.022
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    1. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    2. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    3. Zhang, Wenyang & Peng, Heng, 2010. "Simultaneous confidence band and hypothesis test in generalised varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1656-1680, August.
    4. Li, Jialiang & Zhang, Wenyang, 2011. "A Semiparametric Threshold Model for Censored Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 685-696.
    5. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    6. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    7. Wang, Lan & Kai, Bo & Li, Runze, 2009. "Local Rank Inference for Varying Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1631-1645.
    8. Daryl Pregibon, 1980. "Goodness of Link Tests for Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(1), pages 15-24, March.
    9. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
    10. 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.
    11. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    12. J. Fan & M. Farmen & I. Gijbels, 1998. "Local maximum likelihood estimation and inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 591-608.
    13. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    14. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    15. Li, Qi & Racine, Jeffrey S., 2010. "Smooth Varying-Coefficient Estimation And Inference For Qualitative And Quantitative Data," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1607-1637, December.
    16. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    17. Cheng, Ming-Yen & Zhang, Wenyang & Chen, Lu-Hung, 2009. "Statistical Estimation in Generalized Multiparameter Likelihood Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1179-1191.
    18. C. N. Kuruwita & K. B. Kulasekera & C. M. Gallagher, 2011. "Generalized varying coefficient models with unknown link function," Biometrika, Biometrika Trust, vol. 98(3), pages 701-710.
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    Cited by:

    1. Lili Yue & Gaorong Li & Heng Lian, 2019. "Identification and estimation in quantile varying-coefficient models with unknown link function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1251-1275, December.
    2. Lin, Huazhen & Pan, Lixian & Lv, Shaogao & Zhang, Wenyang, 2018. "Efficient estimation and computation for the generalised additive models with unknown link function," Journal of Econometrics, Elsevier, vol. 202(2), pages 230-244.
    3. Xu, Meng & Li, Jialiang & Chen, Ying, 2017. "Varying coefficient functional autoregressive model with application to the U.S. treasuries," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 168-183.

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    More about this item

    Keywords

    Generalised varying-coefficient models; Identifiability; Iterative estimation procedure; Kernel smoothing; Weighted least squares;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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