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The Oracle Inequalities on Simultaneous Lasso and Dantzig Selector in High-Dimensional Nonparametric Regression
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-06
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
During the last few years, a great deal of attention has been focused on Lasso and Dantzig selector in high-dimensional linear regression when the number of variables can be much larger than the sample size.
Under a sparsity scenario, the authors (see, e.g., Bickel et al., 2009, Bunea et al., 2007, Candes and Tao, 2007, Candès and Tao, 2007, Donoho et al., 2006, Koltchinskii, 2009, Koltchinskii, 2009, Meinshausen and Yu, 2009, Rosenbaum and Tsybakov, 2010, Tsybakov, 2006, van de Geer, 2008, and Zhang and Huang, 2008) discussed the relations between Lasso and Dantzig selector and derived sparsity oracle inequalities for the prediction risk and bounds on the Lp estimation loss.
In this paper, we point out that some of the authors overemphasize the role of some sparsity conditions, and the assumptions based on this sparsity condition may cause bad results.
We give better assumptions and the methods that avoid using the sparsity condition.
As a comparison with the results by Bickel et al., 2009, more precise oracle inequalities for the prediction risk and bounds on the Lp estimation loss are derived when the number of variables can be much larger than the sample size.
American Psychological Association (APA)
Wang, Shiqing& Su, Limin. 2013. The Oracle Inequalities on Simultaneous Lasso and Dantzig Selector in High-Dimensional Nonparametric Regression. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-1031984
Modern Language Association (MLA)
Wang, Shiqing& Su, Limin. The Oracle Inequalities on Simultaneous Lasso and Dantzig Selector in High-Dimensional Nonparametric Regression. Mathematical Problems in Engineering No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-1031984
American Medical Association (AMA)
Wang, Shiqing& Su, Limin. The Oracle Inequalities on Simultaneous Lasso and Dantzig Selector in High-Dimensional Nonparametric Regression. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-1031984
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1031984