Deconvolution in Nonparametric Statistics

Abstract. In this tutorial paper we give an overview of deconvolution problems in nonparametric statistics. First, we consider the problem of density estimation given a contaminated sample. We illustrate that the classical Rosenblatt-Parzen kernel density estimator is unable to capture the full shape of the density while the presented method experiences almost no problems. Second, we use the previous estimator in a nonparametric regression framework with errors-in-variables.