Sparsity oracle inequalities for the Lasso
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Open Access
- 1 January 2007
- journal article
- Published by Institute of Mathematical Statistics in Electronic Journal of Statistics
- Vol. 1 (none) , 169-194
- https://doi.org/10.1214/07-ejs008
Abstract
This paper studies oracle properties of ℓ1-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in terms of the number of non-zero components of the oracle vector. The results are valid even when the dimension of the model is (much) larger than the sample size and the regression matrix is not positive definite. They can be applied to high-dimensional linear regression, to nonparametric adaptive regression estimation and to the problem of aggregation of arbitrary estimators.Keywords
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