Adaptive nonparametric estimation of a component density in a two-class mixture model

Gaëlle Chagny (1) , Antoine Channarond (1) , van Ha Hoang (1) , Angelina Roche (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly weighted kernel estimator with a fully data-driven bandwidth selection method, in the spirit of the Goldenshluger and Lepski method. An oracle-type inequality for the pointwise quadratic risk is derived as well as convergence rates over Hölder smoothness classes. The theoretical results are illustrated by numerical simulations.

Domaines: Théorie [stat.TH]; Applications [stat.AP]

Gaëlle Chagny, Antoine Channarond, van Ha Hoang, Angelina Roche. Adaptive nonparametric estimation of a component density in a two-class mixture model. 2020. ⟨hal-02909601v1⟩