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Variable selection in robust regression models for longitudinal data

Listed author(s):
  • Fan, Yali
  • Qin, Guoyou
  • Zhu, Zhongyi
Registered author(s):

    In this article, we consider variable selection in robust regression models for longitudinal data. We propose a penalized robust estimating equation to estimate the regression parameters and to select the important covariate variables simultaneously. Under some regularity conditions, we show the oracle properties of the proposed robust variable selection methods. A simulation study shows the robustness of the proposed methods against outliers. Moreover, it is found by the simulation study that incorporating the correlation structure into the procedure of variable selection will lead to better performance than ignoring the correlation structure for longitudinal data. In the end, the proposed methods are illustrated in the analysis of a real data set.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12000760
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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 109 (2012)
    Issue (Month): C ()
    Pages: 156-167

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    Handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:156-167
    DOI: 10.1016/j.jmva.2012.03.007
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    1. 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.
    2. Eva Cantoni & Joanna Mills Flemming & Elvezio Ronchetti, 2005. "Variable Selection for Marginal Longitudinal Generalized Linear Models," Biometrics, The International Biometric Society, vol. 61(2), pages 507-514, 06.
    3. Wei Pan, 2001. "Akaike's Information Criterion in Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 57(1), pages 120-125, 03.
    4. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    5. 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.
    6. Johnson, Brent A. & Lin, D.Y. & Zeng, Donglin, 2008. "Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 672-680, June.
    7. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768.
    8. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320.
    9. Wenjiang J. Fu, 2003. "Penalized Estimating Equations," Biometrics, The International Biometric Society, vol. 59(1), pages 126-132, 03.
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