Moderate Deviations Analysis of Binary Hypothesis Testing

TL;DR

This paper develops a refined concentration inequality for discrete-parameter martingales to analyze the moderate deviations in binary hypothesis testing, connecting it to the moderate deviations principle and relative entropy.

Contribution

It introduces a new concentration inequality that refines Azuma-Hoeffding bounds for binary hypothesis testing analysis.

Findings

Refined concentration inequality for martingales with bounded jumps

Connections established between moderate deviations and relative entropy

Enhanced understanding of hypothesis testing error probabilities

Abstract

This paper is focused on the moderate-deviations analysis of binary hypothesis testing. The analysis relies on a concentration inequality for discrete-parameter martingales with bounded jumps, where this inequality forms a refinement to the Azuma-Hoeffding inequality. Relations of the analysis to the moderate deviations principle for i.i.d. random variables and to the relative entropy are considered.