On goodness-of-fit tests for arbitrary multivariate models

TL;DR

This paper develops methods for constructing goodness-of-fit tests applicable to any multivariate distribution or data model, addressing a gap in existing non-parametric testing tools.

Contribution

It introduces a framework for creating goodness-of-fit tests for arbitrary multivariate models, extending beyond univariate cases.

Findings

Provides a general approach for multivariate goodness-of-fit testing

Enables detection of unknown signals in complex data

Supports setting limits on proposed multivariate signal distributions

Abstract

Goodness-of-fit tests are often used in data analysis to test the agreement of a distribution to a set of data. These tests can be used to detect an unknown signal against a known background or to set limits on a proposed signal distribution in experiments contaminated by poorly understood backgrounds. Out-of-the-box non-parametric tests that can target any proposed distribution are only available in the univariate case. In this paper, we discuss how to build goodness-of-fit tests for arbitrary multivariate distributions or multivariate data generation models.