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.
Original language | English |
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Pages (from-to) | 79-96 |
Number of pages | 18 |
Journal | Journal of Multivariate Analysis |
Volume | 167 |
DOIs | |
Publication status | Published - Sept 2018 |
Keywords
- Cox proportional
- Empirical process
- Hazard model
- Lasso
- Mutual coherence
- Oracle property
- Sparse recovery
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty