K-2 rotated goodness-of-fit for multivariate data

TL;DR

This paper introduces a unified goodness-of-fit testing approach for multivariate data that simplifies multiple model comparisons into a single reference distribution test, reducing computational effort.

Contribution

It proposes a method to map tests for various models into a single test for a reference distribution, enabling efficient and valid inference across multiple models.

Findings

Unified testing framework for multiple models

Reduced computational time through simple reference distribution

Valid inference for diverse multivariate models

Abstract

Consider a set of multivariate distributions, $F_1,\dots,F_M$, aiming to explain the same phenomenon. For instance, each $F_m$ may correspond to a different candidate background model for calibration data, or to one of many possible signal models we aim to validate on experimental data. In this article, we show that tests for a wide class of apparently different models $F_{m}$ can be mapped into a single test for a reference distribution $Q$. As a result, valid inference for each $F_m$ can be obtained by simulating \underline{only} the distribution of the test statistic under $Q$. Furthermore, $Q$ can be chosen conveniently simple to substantially reduce the computational time.