Sparsity considerations for dependent variables

Abstract

The aim of this paper is to provide a comprehensive introduction for the study of ℓ₁-penalized estimators in the context of dependent observations. We define a general ℓ₁-penalized estimator for solving problems of stochastic optimization. This estimator turns out to be the LASSO [Tib96] in the regression estimation setting. Powerful theoretical guarantees on the statistical performances of the LASSO were provided in recent papers, however, they usually only deal with the iid case. Here, we study this estimator under various dependence assumptions.