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

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