Density deconvolution from repeated measurements without symmetry assumption on the errors

We consider deconvolution from repeated observations with unknown error distribution. Until now, this model has mostly been studied under the additional assumption that the errors are symmetric.We construct an estimator for the non-symmetric error case and study its theoretical properties and practical performance. It is interesting to note that we can improve substantially upon the rates of convergence which have been presented in the literature and, at the same time, dispose of most of the extremely restrictive assumptions which have been imposed so far.