SICA for Cox's Proportional Hazards Model with a Diverging Number of Parameters

作     者：Yue-Yong SHI Yong-Xiu CAO Yu-Ling JIAO Yan-Yan LIU 

作者机构：School of Mathematics and StatisticsWuhan University 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2014年第30卷第4期

页      面：887-902页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.11171263) 

主　　题：Cox proportional hazards models penalized partial likelihood diverging parameters oracle prop-erty smoothing quasi-Newton 

摘      要：The smooth integration of counting and absolute deviation （SICA） penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan （2009）. In this article, we extend their idea to Cox＇s proportional hazards （PH） model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-Newton （SQN） algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.