ORACLE INEQUALITIES FOR LASSO AND DANTZIG SELECTOR IN HIGH-DIMENSIONAL LINEAR REGRESSION

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.