Adaptive non-asymptotic confidence balls in density estimation

Matthieu Lerasle (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n≥2 and the balls are adaptive over a collection of linear spaces.

Mots clés: resampling methods; Confidence balls; density estimation; resampling methods.

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

Matthieu Lerasle. Adaptive non-asymptotic confidence balls in density estimation. ESAIM: Probability and Statistics, 2012, 16 (1), ps0852. ⟨10.1051/ps/2010012⟩. ⟨hal-00913641⟩