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M-estimation and B-spline approximation for varying coefficient models with longitudinal data

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  • Tang Qingguo
  • Cheng Longsheng

Abstract

A global smoothing procedure is developed using B-spline function approximations for estimating the unknown functions of a varying coefficient model with repeated measurements. A general formulation is used to treat mean, median, quantile and robust mean regressions in one setting. The global convergence rates of the M-estimators of unknown coefficient functions are established. The asymptotic distributes of M-estimators are derived and the approximate confidence intervals are also established. Various applications of the main results, including estimating conditional quantile coefficient functions and robustifying the mean regression coefficient functions are given. Finite sample properties of our procedures are studied through Monte Carlo simulations.

Suggested Citation

  • Tang Qingguo & Cheng Longsheng, 2008. "M-estimation and B-spline approximation for varying coefficient models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 611-625.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:7:p:611-625
    DOI: 10.1080/10485250802375950
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    References listed on IDEAS

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    1. R. L. Eubank & Chunfeng Huang & Y. Muñoz Maldonado & Naisyin Wang & Suojin Wang & R. J. Buchanan, 2004. "Smoothing spline estimation in varying‐coefficient models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 653-667, August.
    2. Xue, Liugen & Zhu, Lixing, 2007. "Empirical Likelihood for a Varying Coefficient Model With Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 642-654, June.
    3. J. Fan & J.‐T. Zhang, 2000. "Two‐step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
    4. Chiang C-T. & Rice J. A & Wu C. O, 2001. "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 605-619, June.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Zhang, Wenyang & Lee, Sik-Yum, 2000. "Variable Bandwidth Selection in Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 116-134, July.
    7. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
    8. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
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    Cited by:

    1. Tadao Hoshino, 2014. "Quantile regression estimation of partially linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 509-536, September.
    2. Tang Qingguo & Cheng Longsheng, 2010. "B-spline estimation for spatial data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 197-217.
    3. Peixin Zhao & Liugen Xue, 2011. "Variable selection for varying coefficient models with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 231-245, September.
    4. Yang, Yiping & Li, Gaorong & Peng, Heng, 2014. "Empirical likelihood of varying coefficient errors-in-variables models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 1-18.
    5. Na Li & Xingzhong Xu & Xuhua Liu, 2011. "Testing the constancy in varying-coefficient regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(3), pages 409-438, November.
    6. 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.

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