Optimal model selection in density estimation

Matthieu Lerasle (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to $1$. We compare the practical performances of these methods in a short simulation study.

Mots clés: Density estimation; optimal model selection; resampling methods; slope heuristic.; slope heuristic

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

Matthieu Lerasle. Optimal model selection in density estimation. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2012, 48 (3), pp.884--908. ⟨10.1214/11-AIHP425⟩. ⟨hal-00422655⟩