ORACLE INEQUALITIES FOR LASSO AND DANTZIG SELECTOR IN HIGH-DIMENSIONAL LINEAR REGRESSION
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2014, Vol 9, Issue 7
Abstract
During the last few years, a great deal attention has been focused on lasso and Dantzig selector in high-dimensional linear regression under a sparsity scenario, that is, when the number of variables can be much larger than the sample size. The authors [4][11][12] derived sparsity oracle inequalities of lasso and Dantzig selector for the prediction risk and bounds on the estimation loss under a variety of assumptions. In this paper, we take the restricted eigenvalue conditions, compatibility condition and UDP condition for examples to show oracle inequalities about lasso and Dantzig selector for high-dimensional linear regression.
Authors and Affiliations
Shiqing Wang, Wenfang Shi
Keywords
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- EP ID EP651451
- DOI 10.24297/jam.v9i7.2313
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