An estimation method for the chi-square divergence with application to test of hypotheses

TL;DR

This paper introduces a new chi-square divergence measure based on convexity and duality, enhancing robustness and applicability in hypothesis testing for contingency tables and parametric models.

Contribution

It proposes a novel definition of chi-square divergence suitable for classical and robust hypothesis testing applications.

Findings

Effective in testing linear constraints

Robust against inliers in parametric models

Applicable to finite and infinite constraint scenarios

Abstract

We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of contingency tables and for the statistical tests for parametric models, for which it has been advocated to be robust against inliers. We present two applications in testing. In the first one we deal with tests for finite and infinite numbers of linear constraints, while, in the second one, we apply {\chi}^2-methodology for parametric testing against contamination.