Work

Sparsity oracle inequalities for the Lasso

Year: 2007

Type: article

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.

Source: Electronic Journal of Statistics

DOI: 10.1214/07-ejs008

Authors: Florentina Bunea, Alexandre Tsybakov, Marten Wegkamp

Institutions: Florida State University, Laboratoire de Probabilités et Modèles Aléatoires

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: National Science Foundation