A new set of tools for goodness-of-fit validation

TL;DR

This paper presents two innovative tools based on the comparison curve for assessing the validity of statistical distributions, including a graphical bar plot and a powerful chi-squared type test, with adaptive component selection.

Contribution

The paper introduces a novel comparison curve-based framework for goodness-of-fit validation, including a new graphical tool and an adaptive chi-squared test, improving model assessment accuracy.

Findings

The new goodness-of-fit tests are competitive with existing methods in power.

The graphical B plot provides detailed visual insights into model validity.

Adaptive component selection enhances test effectiveness.

Abstract

We introduce two new tools to assess the validity of statistical distributions. These tools are based on components derived from a new statistical quantity, the $comparison$ $curve$. The first tool is a graphical representation of these components on a $bar$ $plot$ (B plot), which can provide a detailed appraisal of the validity of the statistical model, in particular when supplemented by acceptance regions related to the model. The knowledge gained from this representation can sometimes suggest an existing $goodness$-$of$-$fit$ test to supplement this visual assessment with a control of the type I error. Otherwise, an adaptive test may be preferable and the second tool is the combination of these components to produce a powerful $\chi^2$-type goodness-of-fit test. Because the number of these components can be large, we introduce a new selection rule to decide, in a data driven fashion, on their proper number to take into consideration. In a simulation, our goodness-of-fit tests are seen to be powerwise competitive with the best solutions that have been recommended in the context of a fully specified model as well as when some parameters must be estimated. Practical examples show how to use these tools to derive principled information about where the model departs from the data.