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Variable selection in quantile varying coefficient models with longitudinal data

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  • Tang, Yanlin
  • Wang, Huixia Judy
  • Zhu, Zhongyi
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    Abstract

    In this paper, we develop a new variable selection procedure for quantile varying coefficient models with longitudinal data. The proposed method is based on basis function approximation and a class of group versions of the adaptive LASSO penalty, which penalizes the Lγ norm of the within-group coefficients with γ≥1. We show that with properly chosen adaptive group weights in the penalization, the resulting penalized estimators are consistent in variable selection, and the estimated functional coefficients retain the optimal convergence rate of nonparametric estimators under the true model. We assess the finite sample performance of the proposed procedure by an extensive simulation study, and the analysis of an AIDS data set and a yeast cell-cycle gene expression data set.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002897
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 57 (2013)
    Issue (Month): 1 ()
    Pages: 435-449

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    Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:435-449

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Adaptive LASSO; Basis spline; Longitudinal data; Penalized estimation;

    References

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    1. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
    2. 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.
    3. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    4. 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.
    5. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
    6. Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(03), pages 478-493, June.
    7. 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.
    8. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    9. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    10. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    11. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    12. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    13. 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.
    14. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    15. Lan Wang & Annie Qu, 2009. "Consistent model selection and data-driven smooth tests for longitudinal data in the estimating equations approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 177-190.
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    Cited by:
    1. Jiang, Rong & Zhou, Zhan-Gong & Qian, Wei-Min & Chen, Yong, 2013. "Two step composite quantile regression for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 180-191.

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