Informative Goodness-of-Fit for Multivariate Distributions

TL;DR

This paper presents an informative goodness-of-fit method for multivariate distributions that identifies sources of mismodeling, providing deeper insights into deviations from the true distribution, especially useful in physics and astronomy.

Contribution

It introduces an innovative iGOF approach utilizing smooth tests and random fields theory to analyze multivariate data and detect background mismodeling.

Findings

High power for various alternative hypotheses

Effective in identifying sources of mismodeling

Applicable to physics and astronomy data

Abstract

This article introduces an informative goodness-of-fit (iGOF) approach to study multivariate distributions. When the null model is rejected, iGOF allows us to identify the underlying sources of mismodeling and naturally equips practitioners with additional insights on the nature of the deviations from the true distribution. The informative character of the procedure is achieved by exploiting smooth tests and random fields theory to facilitate the analysis of multivariate data. Simulation studies show that iGOF enjoys high power for different types of alternatives. The methods presented here directly address the problem of background mismodeling arising in physics and astronomy. It is in these areas that the motivation of this work is rooted.