Regularization for Coxs proportional hazards model with NP-dimensionality

Jelena Bradic Jianqing Fan Jiancheng Jiang

Statistics Theory and Methods mathscidoc:1912.43302

Annals of statistics, 39, (6), 3092, 2011
High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of non-concave penalized methods for non-polynomial (NP) dimensional data with censoring in the framework of Coxs proportional hazards model. A class of folded-concave penalties are employed and both LASSO and SCAD are discussed specifically. We unveil the question under which dimensionality and correlation restrictions can an oracle estimator be constructed and grasped. It is demonstrated that non-concave penalties lead to significant reduction of the irrepresentable condition needed for LASSO model selection consistency. The large deviation result for martingales, bearing interests of its own, is developed for characterizing
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@inproceedings{jelena2011regularization,
  title={Regularization for Coxs proportional hazards model with NP-dimensionality},
  author={Jelena Bradic, Jianqing Fan, and Jiancheng Jiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113602043812862},
  booktitle={Annals of statistics},
  volume={39},
  number={6},
  pages={3092},
  year={2011},
}
Jelena Bradic, Jianqing Fan, and Jiancheng Jiang. Regularization for Coxs proportional hazards model with NP-dimensionality. 2011. Vol. 39. In Annals of statistics. pp.3092. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113602043812862.
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