Submitted to the Statistical Science High-dimensional regression with unknown variance

Abstract. We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is put on non-asymptotic analyses and feasible procedures. In addition, a small numerical study compares the practical performance of three schemes for tuning the Lasso estima-tor and some references are collected for some more general models, including multivariate regression and nonparametric regression