On the sign consistency of the Lasso for the high-dimensional Cox model

JOURNAL OF MULTIVARIATE ANALYSIS

卷:167

Article

Lv, Shaogao^1,2  You, Mengying^1,2  Lin, Huazhen^1,2  Lian, Heng³  Huang, Jian^4,5 

[1] Southwestern Univ Finance & Econ, Ctr Stat Res, Chengdu 611130, Sichuan, Peoples R China

[2] Southwestern Univ Finance & Econ, Sch Stat, Chengdu 611130, Sichuan, Peoples R China

[3] City Univ Hong Kong, Dept Math, Kowloon Tong, Hong Kong, Peoples R China

[4] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Hong Kong, Peoples R China

[5] Univ Iowa, Dept Stat & Actuarial Sci, Iowa City, IA 52242 USA

关键词: Cox proportional;    Empirical process;    Hazard model;    Lasso;    Mutual coherence;    Oracle property;    Sparse recovery;   

DOI  :  10.1016/j.jmva.2018.04.005

来源: Elsevier

【 摘 要 】

In this paper we study the l(1)-penalized partial likelihood estimator for the sparse high dimensional Cox proportional hazards model. In particular, we investigate how the l(1)-penalized partial likelihood estimation recovers the sparsity pattern and the conditions under which the sign support consistency is guaranteed. We establish sign recovery consistency and l(infinity)-error bounds for the Lasso partial likelihood estimator under suitable and interpretable conditions, including mutual incoherence conditions. More importantly, we show that the conditions of the incoherence and bounds on the minimal non-zero coefficients are necessary, which provides significant and instructional implications for understanding the Lasso for the Cox model. Numerical studies are presented to illustrate the theoretical results. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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