KMS Of Academy of mathematics and systems sciences, CAS
| ORACLE INEQUALITIES AND SELECTION CONSISTENCY FOR WEIGHTED LASSO IN HIGH-DIMENSIONAL ADDITIVE HAZARDS MODEL | |
Zhang, Haixiang1; Sun, Liuquan2 ; Zhou, Yong3; Huang, Jian4
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| 2017-10-01 | |
| Source Publication | STATISTICA SINICA
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| ISSN | 1017-0405 |
| Volume | 27Issue:4Pages:1903-1920 |
| Abstract | 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. |
| Keyword | High-dimensional covariates oracle inequalities sign consistency survival analysis variable selection |
| DOI | 10.5705/ss.202015.0075 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Statistics & Probability |
| WOS ID | WOS:000412035100027 |
| Publisher | STATISTICA SINICA |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/26658 |
| Collection | 应用数学研究所 |
| Corresponding Author | Zhang, Haixiang |
| Affiliation | 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 |
| Recommended Citation 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. |
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