Nonparametric Regression using the Concept of Minimum Energy

TL;DR

This paper introduces a nonparametric regression method based on minimizing the energy of multivariate data sets, enabling parameter estimation without assuming specific distribution forms.

Contribution

It extends the energy-based goodness-of-fit test to a regression framework for multiple multivariate data sets, allowing parameter inference without parametric models.

Findings

Effective in simple example analyses

Does not require parametric distribution assumptions

Shows promising potential for multivariate data analysis

Abstract

It has recently been shown that an unbinned distance-based statistic, the energy, can be used to construct an extremely powerful nonparametric multivariate two sample goodness-of-fit test. An extension to this method that makes it possible to perform nonparametric regression using multiple multivariate data sets is presented in this paper. The technique, which is based on the concept of minimizing the energy of the system, permits determination of parameters of interest without the need for parametric expressions of the parent distributions of the data sets. The application and performance of this new method is discussed in the context of some simple example analyses.