On the sign consistency of the Lasso for the high-dimensional Cox model
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
Original language | English |
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Pages (from-to) | 79-96 |
Journal / Publication | Journal of Multivariate Analysis |
Volume | 167 |
Online published | 22 Apr 2018 |
Publication status | Published - Sept 2018 |
Link(s)
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.
Research Area(s)
- Cox proportional, Empirical process, Hazard model, Lasso, Mutual coherence, Oracle property, Sparse recovery
Citation Format(s)
On the sign consistency of the Lasso for the high-dimensional Cox model. / Lv, Shaogao; You, Mengying; Lin, Huazhen et al.
In: Journal of Multivariate Analysis, Vol. 167, 09.2018, p. 79-96.
In: Journal of Multivariate Analysis, Vol. 167, 09.2018, p. 79-96.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review