Exhaustive goodness-of-fit via smoothed inference and graphics

TL;DR

This paper introduces a comprehensive framework for goodness-of-fit testing that combines modeling, estimation, inference, and visualization, using smooth tests, a smoothed bootstrap, and an innovative CD-plot for detailed analysis.

Contribution

It presents a novel formulation of smooth goodness-of-fit tests applicable to any distribution, along with a new graphical tool and bootstrap method for enhanced inference and model diagnostics.

Findings

Framework effectively integrates modeling, inference, and visualization.

Smooth tests extend to arbitrary distributions, continuous or discrete.

CD-plot provides detailed graphical summaries of goodness-of-fit.

Abstract

Classical tests of goodness-of-fit aim to validate the conformity of a postulated model to the data under study. Given their inferential nature, they can be considered a crucial step in confirmatory data analysis. In their standard formulation, however, they do not allow exploring how the hypothesized model deviates from the truth nor do they provide any insight into how the rejected model could be improved to better fit the data. The main goal of this work is to establish a comprehensive framework for goodness-of-fit which naturally integrates modeling, estimation, inference, and graphics. Modeling and estimation focus on a novel formulation of smooth tests that easily extends to arbitrary distributions, either continuous or discrete. Inference and adequate post-selection adjustments are performed via a specially designed smoothed bootstrap and the results are summarized via an exhaustive graphical tool called CD-plot.