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 nonasymptotic analyses and feasible procedures. In addition, a small numerical study compares the practical performance of three schemes for tuning the lasso estimator and some references are collected for some more general models, including multivariate regression and nonparametric regression.
"High-Dimensional Regression with Unknown Variance." Statist. Sci. 27 (4) 500 - 518, November 2012. https://doi.org/10.1214/12-STS398