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Adaptive LASSO for general transformation models with right censored data

  • Li, Jianbo
  • Gu, Minggao
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    In this paper, we consider variable selection for general transformation models with right censored data and propose a unified procedure for both variable selection and estimation. We conduct the proposed procedure by maximizing penalized log-marginal likelihood function with Adaptive LASSO penalty (ALASSO) on regression coefficients. Two main advantages of this procedure are as follows: (i) the penalties can be assigned to regression coefficients adaptively by data according to the importance of corresponding covariates; (ii) it is free of baseline survival function and censoring distribution. Under some regular conditions, we show that the penalized estimates with ALASSO are n-consistent and enjoy oracle properties. Some simulation examples and Primary Biliary Cirrhosis Data application illustrate that our proposed procedure works very well for moderate sample size.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312001053
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 8 ()
    Pages: 2583-2597

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2583-2597
    DOI: 10.1016/j.csda.2012.02.023
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. 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.
    2. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    3. 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.
    4. 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.
    5. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
    6. Anestis Antoniadis & Piotr Fryzlewicz & Frédérique Letué, 2010. "The Dantzig selector in Cox's proportional hazards model," LSE Research Online Documents on Economics 30992, London School of Economics and Political Science, LSE Library.
    7. Anestis Antoniadis & Piotr Fryzlewicz & Frédérique Letué, 2010. "The Dantzig Selector in Cox's Proportional Hazards Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 531-552.
    8. Zhang, Hao Helen & Lu, Wenbin & Wang, Hansheng, 2010. "On sparse estimation for semiparametric linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1594-1606, August.
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