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

Abstract:

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 oracletype 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.

Joint work with Gaëlle Chagny, Antoine Channarond (University of Rouen - Normandie) and Angelina Roche (Paris Dauphine University)