A Goodness-of-Fit Test for Statistical Models

TL;DR

This paper introduces a new framework for goodness-of-fit testing in statistical models by connecting it with two-sample distribution comparison, enabling evaluation of various models' usefulness for data analysis.

Contribution

It proposes a novel approach linking goodness-of-fit testing to two-sample comparison, broadening the applicability of model evaluation methods.

Findings

Effective in evaluating a wide range of models

Demonstrates good performance through examples

Provides a flexible framework for model assessment

Abstract

Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to make some of them be useful. The question here is how can we measure the usefulness of a statistical model for the data in hand? This is key to statistical prediction. The important statistical problem of testing whether the observations follow the proposed statistical model has only attracted relatively few attentions. In this paper, we proposed a new framework for this problem through building its connection with two-sample distribution comparison. The proposed method can be applied to evaluate a wide range of models. Examples are given to show the performance of the proposed method.