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Variable selection and structure identification for varying coefficient Cox models

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  • Honda, Toshio
  • Yabe, Ryota

Abstract

We consider varying coefficient Cox models with high-dimensional covariates. We apply the group Lasso to these models and propose a variable selection procedure. Our procedure can cope with simultaneous variable selection and structure identification for high-dimensional varying coefficient models to find true semi-varying coefficient models from them. We also derive an oracle inequality and closely examine restrictive eigenvalue conditions. We focus on Cox models with time-varying coefficients. The theoretical results on variable selection can be extended easily to some other important models which we only mention briefly since they can be treated in the same way. The models considered here are the most popular among structured nonparametric regression models. The results of numerical studies are also reported.

Suggested Citation

  • Honda, Toshio & Yabe, Ryota, 2017. "Variable selection and structure identification for varying coefficient Cox models," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 103-122.
    • Handle: RePEc:eee:jmvana:v:161:y:2017:i:c:p:103-122
    DOI: 10.1016/j.jmva.2017.07.007
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    References listed on IDEAS

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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. Heng Lian & Peng Lai & Hua Liang, 2013. "Partially Linear Structure Selection in Cox Models with Varying Coefficients," Biometrics, The International Biometric Society, vol. 69(2), pages 348-357, June.
    3. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
    4. Rui Song & Wenbin Lu & Shuangge Ma & X. Jessie Jeng, 2014. "Censored rank independence screening for high-dimensional survival data," Biometrika, Biometrika Trust, vol. 101(4), pages 799-814.
    5. Tang, Yanlin & Song, Xinyuan & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in high-dimensional quantile varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 115-132.
    6. S. Wang & B. Nan & N. Zhu & J. Zhu, 2009. "Hierarchically penalized Cox regression with grouped variables," Biometrika, Biometrika Trust, vol. 96(2), pages 307-322.
    7. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    8. Zongwu Cai & Yanqing Sun, 2003. "Local Linear Estimation for Time‐Dependent Coefficients in Cox's Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 93-111, March.
    9. Jun Yan & Jian Huang, 2012. "Model Selection for Cox Models with Time-Varying Coefficients," Biometrics, The International Biometric Society, vol. 68(2), pages 419-428, June.
    10. Guilloux, Agathe & Lemler, Sarah & Taupin, Marie-Luce, 2016. "Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 141-159.
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    Cited by:

    1. Akira Shinkyu, 2023. "Forward Selection for Feature Screening and Structure Identification in Varying Coefficient Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 485-511, February.
    2. Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
    3. Honda, Toshio & 本田, 敏雄, 2019. "The de-biased group Lasso estimation for varying coefficient models," Discussion Papers 2018-04, Graduate School of Economics, Hitotsubashi University.
    4. 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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