A0301
Title: Adaptive estimation of the nonparametric component under a two-class mixture model
Authors: Gaelle Chagny - CNRS, Université de Rouen Normandie (France) [presenting]
Antoine Channarond - Universite de Rouen (France)
Van Ha Hoang - University of Science Vietnam National University in Ho Chi Minh City (Vietnam)
Angelina Roche - Universite Paris Dauphine (France)
Abstract: A two-class mixture model is considered, where the density of one of the components is known (equal to the uniform density on the interval $[0; 1]$). This problem appears in many statistical settings, robust estimation and multiple testing among others. 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. Its definition involves empirical counterparts both for the mixture density and the mixing proportion: preliminary estimators for these quantities are also proposed. An oracle-type inequality for the pointwise quadratic risk is derived as well as convergence rates over Holder smoothness classes. The theoretical results are illustrated by numerical simulations.
