Moderate deviation principle for the chi-square statistics

TL;DR

This paper establishes a moderate deviation principle for the Pearson chi-square statistic when the alphabet size varies with sample size, providing insights into its probabilistic behavior under dynamic conditions.

Contribution

It introduces a moderate deviation principle for chi-square statistics with a dynamically changing alphabet, extending existing theory to more realistic, evolving scenarios.

Findings

Established the moderate deviation principle for the statistic.

Extended theoretical understanding to dynamic alphabet scenarios.

Provides a foundation for statistical inference in evolving categorical data.

Abstract

In the present paper, we consider the Pearson chi-square statistic defined on a finite alphabet which is assumed to dynamically vary as the sample size increases, and establish its moderate deviation principle.