Density deconvolution from repeated measurements without symmetry assumption on the errors

TL;DR

This paper develops a new estimator for density deconvolution using repeated measurements without assuming symmetric errors, improving convergence rates and relaxing previous restrictive assumptions.

Contribution

It introduces a novel estimator for non-symmetric error deconvolution and demonstrates improved theoretical convergence rates and practical performance.

Findings

Enhanced convergence rates over previous methods

Effective handling of non-symmetric error distributions

Robust estimator with practical applicability

Abstract

We consider deconvolution from repeated observations with unknown error distribution. So far, 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 so far been presented in the literature and, at the same time, dispose of most of the extremely restrictive assumptions which have been imposed so far.