REGULARIZATION FOR COX'S PROPORTIONAL HAZARDS MODEL WITH NP-DIMENSIONALITY

• 成果类型: Article
• 署名作者: Bradic, Jelena; Fan, Jianqing; Jiang, Jiancheng
• 署名单位: University of California System; University of California San Diego; University of North Carolina; University of North Carolina Charlotte; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS911
• 发表日期: 2011
• 页码: 3092-3120
• 关键词: nonconcave penalized likelihood; variable selection; exponential inequalities; DANTZIG SELECTOR; Lasso; sparsity; regression; martingales; RECOVERY

摘要

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of nonconcave penalized methods for nonpolynomial (NP) dimensional data with censoring in the framework of Cox's proportional hazards model. A class of folded-concave penalties are employed and both LASSO and SCAD are discussed specifically. We unveil the question under which dimensionality and correlation restrictions can an oracle estimator be constructed and grasped. It is demonstrated that nonconcave penalties lead to significant reduction of the irrepresentable condition needed for LASSO model selection consistency. The large deviation result for martingales, bearing interests of its own, is developed for characterizing the strong oracle property. Moreover, the nonconcave regularized estimator, is shown to achieve asymptotically the information bound of the oracle estimator. A coordinate-wise algorithm is developed for finding the grid of solution paths for penalized hazard regression problems, and its performance is evaluated on simulated and gene association study examples.