Journal article
On the sign consistency of the Lasso for the high-dimensional Cox model
Journal of multivariate analysis, Vol.167, pp.79-96
09/2018
DOI: 10.1016/j.jmva.2018.04.005
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.
Details
- Title: Subtitle
- On the sign consistency of the Lasso for the high-dimensional Cox model
- Creators
- Shaogao Lv - Southwestern University of Finance and EconomicsMengying You - Southwestern University of Finance and EconomicsHuazhen Lin - Southwestern University of Finance and EconomicsHeng Lian - City University of Hong KongJian Huang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of multivariate analysis, Vol.167, pp.79-96
- DOI
- 10.1016/j.jmva.2018.04.005
- ISSN
- 0047-259X
- eISSN
- 1095-7243
- Publisher
- Elsevier Inc
- Grant note
- DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11571282, 11528102; DOI: 10.13039/501100012226, name: Fundamental Research Funds for the Central Universities of China, award: JBK120509, JBK140507, KLAS-130026507
- Language
- English
- Date published
- 09/2018
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257630202771
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