Estimating a Signal In the Presence of an Unknown Background

TL;DR

This paper introduces a method for fitting data distributions when only one component (signal or background) is parametrically known, using non-parametric kernel density estimation to accurately estimate unknown distributions and their parameters.

Contribution

It presents a novel approach combining parametric and non-parametric methods to estimate unknown distributions in data fitting tasks.

Findings

Estimates are unbiased in simulation studies.

Errors on parameter estimates are accurate.

Method effectively handles unknown background distributions.

Abstract

We describe a method for fitting distributions to data which only requires knowledge of the parametric form of either the signal or the background but not both. The unknown distribution is fit using a non-parametric kernel density estimator. The method returns parameter estimates as well as errors on those estimates. Simulation studies show that these estimates are unbiased and that the errors are correct.