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December 2011 Regularization for Cox’s proportional hazards model with NP-dimensionality
Jelena Bradic, Jianqing Fan, Jiancheng Jiang
Ann. Statist. 39(6): 3092-3120 (December 2011). DOI: 10.1214/11-AOS911


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.


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Jelena Bradic. Jianqing Fan. Jiancheng Jiang. "Regularization for Cox’s proportional hazards model with NP-dimensionality." Ann. Statist. 39 (6) 3092 - 3120, December 2011.


Published: December 2011
First available in Project Euclid: 27 January 2012

zbMATH: 1246.62202
MathSciNet: MR3012402
Digital Object Identifier: 10.1214/11-AOS911

Primary: 60G44 , 62N02
Secondary: 60F10 , 62F12

Keywords: hazard rate , large deviation , Lasso , oracle , SCAD

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 6 • December 2011
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