Kernel Estimation in High-Energy Physics

TL;DR

This paper reviews kernel estimation methods for probability density functions, discusses their applications in high-energy physics, compares available software packages, and analyzes their advantages and systematic errors.

Contribution

It provides a comprehensive overview of kernel estimation techniques and their specific applications and challenges in high-energy physics research.

Findings

Kernel estimation offers unbinned, non-parametric density estimates.

Applications in high-energy physics demonstrate practical utility.

Discussion of systematic errors enhances understanding of method limitations.

Abstract

Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of Kernel Estimation is developed for univariate and multivariate settings. The second section discusses some of the applications of Kernel Estimation to high-energy physics. The third section provides an overview of the available univariate and multivariate packages. This paper concludes with a discussion of the inherent advantages of kernel estimation techniques and systematic errors associated with the estimation of parent distributions.