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P-splines quantile regression estimation in varying coefficient models

  • Y. Andriyana
  • I. Gijbels


  • A. Verhasselt
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    Quantile regression, as a generalization of median regression, has been widely used in statistical modeling. To allow for analyzing complex data situations, several flexible regression models have been introduced. Among these are the varying coefficient models, that differ from a classical linear regression model by the fact that the regression coefficients are no longer constant but functions that vary with the value taken by another variable, such as for example, time. In this paper, we study quantile regression in varying coefficient models for longitudinal data. The quantile function is modeled as a function of the covariates and the main task is to estimate the unknown regression coefficient functions. We approximate each coefficient function by means of P-splines. Theoretical properties of the estimators, such as rate of convergence and an asymptotic distribution are established. The estimation methodology requests solving an optimization problem that also involves a smoothing parameter. For a special case the optimization problem can be transformed into a linear programming problem for which then a Frisch–Newton interior point method is used, leading to a computationally fast and efficient procedure. Several data-driven choices of the smoothing parameters are briefly discussed, and their performances are illustrated in a simulation study. Some real data analysis demonstrates the use of the developed method. Copyright Sociedad de Estadística e Investigación Operativa 2014

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    Article provided by Springer in its journal TEST.

    Volume (Year): 23 (2014)
    Issue (Month): 1 (March)
    Pages: 153-194

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    Handle: RePEc:spr:testjl:v:23:y:2014:i:1:p:153-194
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    1. repec:cup:cbooks:9780521608275 is not listed on IDEAS
    2. 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.
    3. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    4. 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.
    5. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    6. Li, Youjuan & Liu, Yufeng & Zhu, Ji, 2007. "Quantile Regression in Reproducing Kernel Hilbert Spaces," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 255-268, March.
    7. Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. repec:cup:cbooks:9780521845731 is not listed on IDEAS
    10. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    11. Lamarche, Carlos, 2010. "Robust penalized quantile regression estimation for panel data," Journal of Econometrics, Elsevier, vol. 157(2), pages 396-408, August.
    12. Anestis Antoniadis & Irène Gijbels & Mila Nikolova, 2011. "Penalized likelihood regression for generalized linear models with non-quadratic penalties," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(3), pages 585-615, June.
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