Rejoinder on: Minimal penalties and the slope heuristics: a survey

Sylvain Arlot (1, 2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 CELESTE - Statistique mathématique et apprentissage

This text is the rejoinder following the discussion of a survey paper about minimal penalties and the slope heuristics (Arlot, 2019. Minimal penalties and the slope heuristics: a survey. Journal de la SFDS). While commenting on the remarks made by the discussants, it provides two new results about the slope heuristics for model selection among a collection of projection estimators in least-squares fixed-design regression. First, we prove that the slope heuristics works even when all models are significantly biased. Second, when the noise is Gaussian with a general dependence structure, we compute expectations of key quantities, showing that the slope heuristics certainly is valid in this setting also.

Mots clés: model selection; scree test; minimal penalty; L-curve heuristics; residual-variance estimation; slope heuristics; Overpenalization; estimator selection; elbow heuristics; penalization

Mots clés: heuristique de coude; estimation de la variance résiduelle; test scree; heuristique de pente; heuristique de courbe en L; sélection d'estimateurs; pénalisation; sélection de modèles; pénalité minimale; surpénalisation

Domaines: Statistiques [math.ST]; Méthodologie [stat.ME]; Autres [stat.ML]; Théorie [stat.TH]

Sylvain Arlot. Rejoinder on: Minimal penalties and the slope heuristics: a survey. Journal de la Société Française de Statistique, 2019, Minimal penalties and the slope heuristics: a survey, 160 (3), pp.158-168. ⟨hal-02300688⟩