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

Shaogao Lv, Mengying You, Huazhen Lin, Heng Lian, Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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 languageEnglish
Pages (from-to)79-96
Number of pages18
JournalJournal of Multivariate Analysis
Volume167
DOIs
Publication statusPublished - 1 Sep 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

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