Simple expressions of the LASSO and SLOPE estimators in small-dimension

Rémi Servien (1) , Patrick J C Tardivel (2) , Didier Concordet (3)

1 INRA - Institut National de la Recherche Agronomique
2 ToxAlim - ToxAlim
3 UTA - Toxicologie Alimentaire

We study the LASSO and SLOPE estimators when the design X satisfies ker(X) = 0. We state that, even if the design is not orthogonal, even if residuals are correlated, up to a transformation, the LASSO and SLOPE estimators have a simple expression based on the best linear unbiased estimator.

Mots clés: Best linear unbiased estimator; LASSO; SLOPE

Domaines: Statistiques [stat]; Mathématiques [math]

Rémi Servien, Patrick J C Tardivel, Didier Concordet. Simple expressions of the LASSO and SLOPE estimators in small-dimension. 2019. ⟨hal-01755076v2⟩