Adaptive density estimation in deconvolution problems with unknown error distribution

Abstract

A density deconvolution problem with unknown distribution of the errors is considered. To make the target density identifiable, one has to assume that some additional information on the noise is available. We consider two different models: the framework where some additional sample of the pure noise is available, as well as the repeated observation model, where the contaminated random variable of interest can be observed repeatedly. We introduce kernel estimators and present upper risk bounds. The focus of this work lies on the optimal data driven choice of the smoothing parameter using a penalization strategy