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ORACLE INEQUALITIES AND SELECTION CONSISTENCY FOR WEIGHTED LASSO IN HIGH-DIMENSIONAL ADDITIVE HAZARDS MODEL

文献类型：期刊论文

作者Zhang, Haixiang1; Sun, Liuquan2; Zhou, Yong3; Huang, Jian4
刊名STATISTICA SINICA
出版日期2017-10-01
卷号27期号:4页码:1903-1920
ISSN号1017-0405
关键词High-dimensional covariates oracle inequalities sign consistency survival analysis variable selection
DOI10.5705/ss.202015.0075
英文摘要The additive hazards model has many applications in high-throughput genomic data analysis and clinical studies. In this article, we study the weighted Lasso estimator for the additive hazards model in sparse, high-dimensional settings where the number of time-dependent covariates is much larger than the sample size. Based on compatibility, cone invertibility factors, and restricted eigenvalues of the Hessian matrix, we establish some non-asymptotic oracle inequalities for the weighted Lasso. Under mild conditions, we show that these quantities are bounded from below by positive constants, thus the compatibility and cone invertibility factors can be treated as positive constants in the oracle inequalities. A multistage adaptive method with weights recursively generated from a concave penalty is presented. We prove a selection consistency theorem and establish an upper bound for dimension of the weighted Lasso estimator.
资助项目National Natural Science Foundation of China[11301212] ; National Natural Science Foundation of China[11401146] ; National Natural Science Foundation of China[11231010] ; National Natural Science Foundation of China[11690015] ; National Natural Science Foundation of China[71331006] ; National Natural Science Foundation of China[91546202] ; China Postdoctoral Science Foundation[2014M550861] ; Key Laboratory of RCSDS, CAS[2008DP173182] ; Innovative Research Team of Shanghai University of Finance and Economics[IRTSHUFE13122402]
WOS研究方向Mathematics
语种英语
出版者STATISTICA SINICA
WOS记录号WOS:000412035100027
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/26657]  
专题应用数学研究所
通讯作者Zhang, Haixiang
作者单位1.Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing, Peoples R China
3.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai 200433, Peoples R China
4.Univ Iowa, Dept Stat & Actuarial Sci, Iowa City, IA 52242 USA
推荐引用方式
GB/T 7714		 Zhang, Haixiang,Sun, Liuquan,Zhou, Yong,et al. ORACLE INEQUALITIES AND SELECTION CONSISTENCY FOR WEIGHTED LASSO IN HIGH-DIMENSIONAL ADDITIVE HAZARDS MODEL[J]. STATISTICA SINICA,2017,27(4):1903-1920.
APA Zhang, Haixiang,Sun, Liuquan,Zhou, Yong,&Huang, Jian.(2017).ORACLE INEQUALITIES AND SELECTION CONSISTENCY FOR WEIGHTED LASSO IN HIGH-DIMENSIONAL ADDITIVE HAZARDS MODEL.STATISTICA SINICA,27(4),1903-1920.
MLA Zhang, Haixiang,et al."ORACLE INEQUALITIES AND SELECTION CONSISTENCY FOR WEIGHTED LASSO IN HIGH-DIMENSIONAL ADDITIVE HAZARDS MODEL".STATISTICA SINICA 27.4(2017):1903-1920.

入库方式： OAI收割

来源：数学与系统科学研究院

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