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On the sign consistency of the Lasso for the high-dimensional Cox model
Journal article   Open access   Peer reviewed

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

Shaogao Lv, Mengying You, Huazhen Lin, Heng Lian and Jian Huang
Journal of multivariate analysis, Vol.167, pp.79-96
09/2018
DOI: 10.1016/j.jmva.2018.04.005
url
https://doi.org/10.1016/j.jmva.2018.04.005View
Published (Version of record) Open Access

Abstract

In this paper we study the ℓ1-penalized partial likelihood estimator for the sparse high-dimensional Cox proportional hazards model. In particular, we investigate how the ℓ1-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∞-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.
Cox proportional Empirical process Hazard model Lasso Mutual coherence Oracle property Sparse recovery

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