Testing distribution in deconvolution problems

TL;DR

This paper introduces a new statistical test for determining the distribution of an unobserved variable contaminated by known additive noise, applicable to both discrete and continuous cases, with practical illustrations.

Contribution

It develops a data-driven test statistic for distribution testing in deconvolution problems that works for both discrete and continuous data.

Findings

Test performs well in simulations

Applicable to both discrete and continuous data

Validated with practical examples

Abstract

In this paper we consider a random variable $Y$ contamined by an independent additive noise $Z$. We assume that $Z$ has known distribution. Our purpose is to test the distribution of the unobserved random variable $Y$. We propose a data driven statistic based on a development of the density of $Y+Z$, which is valid in the discrete case and in the continuous case. The test is illustrated in both cases.