# Density deconvolution under general assumptions on the distribution of measurement errors

## TL;DR

This paper develops a flexible method for density deconvolution that works under broad conditions on measurement error distributions, including cases with zeros in their characteristic functions, improving estimation robustness.

## Contribution

It introduces a novel approach for density deconvolution that handles general error distributions, relaxing the common zero-free characteristic function assumption.

## Key findings

- Derived upper bounds on estimator risk.
- Provided conditions where zeros in characteristic functions do not affect accuracy.
- Showed conditions are necessary in certain cases.

## Abstract

In this paper we study the problem of density deconvolution under general assumptions on the measurement error distribution. Typically deconvolution estimators are constructed using Fourier transform techniques, and it is assumed that the characteristic function of the measurement errors does not have zeros on the real line. This assumption is rather strong and is not fulfilled in many cases of interest. In this paper we develop a methodology for constructing optimal density deconvolution estimators in the general setting that covers vanishing and non--vanishing characteristic functions of the measurement errors. We derive upper bounds on the risk of the proposed estimators and provide sufficient conditions under which zeros of the corresponding characteristic function have no effect on estimation accuracy. Moreover, we show that the derived conditions are also necessary in some specific problem instances.