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 emphasize 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 esti- mator 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. 2011. ⟨hal-00626630v1⟩