Hierarchically penalized additive hazards model with diverging number of parameters  

作　　者：LIU JiCai ZHANG RiQuan ZHAO WeiHua 

机构地区：[1]School of Finance and Statistics,East China Normal University [2]Department of Mathematics,Shanxi Datong University [3]School of Science,Nantong University

出　　处：《Science China Mathematics》2014年第4期873-886,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171112,11101114 and 11201190);National Statistical Science Research Major Program of China(Grant No.2011LZ051)

摘　　要：In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation（SCAD）and adaptive lasso.

关 键 词：additive hazards model group variable selection oracle property diverging parameters two-levelselection 

分 类 号：O212.1[理学—概率论与数理统计]