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

doi:10.5705/ss.202015.0075

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	ORACLE INEQUALITIES AND SELECTION CONSISTENCY FOR WEIGHTED LASSO IN HIGH-DIMENSIONAL ADDITIVE HAZARDS MODEL
	Zhang, Haixiang 1; Sun, Liuquan2 ; Zhou, Yong3 ; Huang, Jian 4
	2017-10-01
发表期刊	STATISTICA SINICA
ISSN	1017-0405
卷号	27 期号:4 页码:1903-1920
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.
关键词	High-dimensional covariates oracle inequalities sign consistency survival analysis variable selection
DOI	10.5705/ss.202015.0075
语种	英语
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
WOS类目	Statistics & Probability
WOS记录号	WOS:000412035100027
出版者	STATISTICA SINICA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26658
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.