High-dimensional regression with unknown variance

Christophe Giraud (1) , Sylvie Huet (2) , Nicolas Verzelen (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Unité MIAJ - INRA - Mathématiques et Informatique Appliquées
3 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

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 estimator and some references are collected for some more general models, including multivariate regression and nonparametric regression.

Mots clés: linear regression; high-dimension; unknown variance

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Giraud, Sylvie Huet, Nicolas Verzelen. High-dimensional regression with unknown variance. 2012. ⟨hal-00626630v2⟩