Chi-squared test for hypothesis testing of homogeneity

TL;DR

This paper establishes the conditions under which chi-squared tests for homogeneity are uniformly consistent as the number of categories grows with sample size, applicable to both densities and distribution functions.

Contribution

It provides necessary and sufficient conditions for the uniform consistency of chi-squared tests for homogeneity with increasing cell counts.

Findings

Conditions for uniform consistency are derived.

Applicability to both density and distribution function frameworks.

Guidelines for increasing cell counts with sample size.

Abstract

We provide necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives of chi-squared test for testing of hypothesis of homogeneity. The number of cells of chi-squared test increases with sample size growth. Nonparametric sets of alternatives can be defined both in terms of densities and distribution functions.