High-Dimensional Regression with Unknown Variance

We review recent results for high-dimensional sparse linear re- gression 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 nonasymptotic analyses and feasible pro- cedures. In addition, a small numerical study compares the practical perfor- mance of three schemes for tuning the lasso estimator and some references are collected for some more general models, including multivariate regres- sion and nonparametric regression.