Moderate deviation theorem for the Neyman-Pearson statistic in testing uniformity

TL;DR

This paper investigates the conditions under which a moderate deviation theorem applies to the Neyman-Pearson statistic for testing uniformity, especially for local alternatives involving unbounded densities, using Mogulskii's inequality.

Contribution

It establishes a sufficient condition for the moderate deviation theorem to hold in the context of uniformity testing with local alternatives.

Findings

MD theorem does not hold for all unbounded densities

A specific condition ensures the MD theorem's validity

Proof utilizes Mogulskii's inequality

Abstract

We show that for local alternatives to uniformity which are determined by a sequence of square integrable densities the moderate deviation (MD) theorem for the corresponding Neyman-Pearson statistic does not hold in the full range for all unbounded densities. We give a sufficient condition under which MD theorem holds. The proof is based on Mogulskii's inequality.