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Variable selection in Cox regression models with varying coefficients

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  • Toshio Honda
  • Wolfgang Karl Härdle

Abstract

We deal with two kinds of Cox regression models with varying coefficients. The coefficients vary with time in one model. In the other model, there is an important random variable called an index variable and the coefficients vary with the variable. In both models, we have p-dimensional covariates and p increases moderately. However, it is the case that only a small part of the covariates are relevant in these situations. We carry out variable selection and estimation of the coefficient functions by using the group SCAD-type estimator and the adaptive group Lasso estimator. We examine the theoretical properties of the estimators, especially the L2 convergence rate, the sparsity, and the oracle property. Simulation studies and a real data analysis show the performance of these new techniques.

Suggested Citation

  • Toshio Honda & Wolfgang Karl Härdle, 2012. "Variable selection in Cox regression models with varying coefficients," SFB 649 Discussion Papers SFB649DP2012-061, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2012-061
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2012-061.pdf
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    References listed on IDEAS

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    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. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    6. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    7. Jianwen Cai & Jianqing Fan & Runze Li & Haibo Zhou, 2005. "Variable selection for multivariate failure time data," Biometrika, Biometrika Trust, vol. 92(2), pages 303-316, June.
    8. 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, February.
    9. Cai, Jianwen & Fan, Jianqing & Jiang, Jiancheng & Zhou, Haibo, 2007. "Partially Linear Hazard Regression for Multivariate Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 538-551, June.
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    Citations

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    Cited by:

    1. HONDA, Toshio & YABE, Ryota, 2017. "Variable selection and structure identification for varying coefficient Cox models," Discussion Papers 2016-05, Graduate School of Economics, Hitotsubashi University.
    2. Ling Zhou & Lu Tang & Angela T. Song & Diane M. Cibrik & Peter X.-K. Song, 2017. "A LASSO Method to Identify Protein Signature Predicting Post-transplant Renal Graft Survival," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 431-452, December.
    3. Ling Zhou & Lu Tang & Angela T. Song & Diane M. Cibrik & Peter X.-K. Song, 0. "A LASSO Method to Identify Protein Signature Predicting Post-transplant Renal Graft Survival," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 0, pages 1-22.
    4. Honda, Toshio, 2019. "The de-biased group Lasso estimation for varying coefficient models," Discussion Papers 2018-04, Graduate School of Economics, Hitotsubashi University.
    5. Toshio Honda, 2021. "The de-biased group Lasso estimation for varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 3-29, February.

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    More about this item

    Keywords

    Cox regression model; high-dimensional data; sparsity; oracle estimator; B-splines; group SCAD; adaptive group Lasso; L2 convergence rate;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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