Asymptotic Formula for a General Double-Bounded Custom-Sided Likelihood Based Test Statistic

TL;DR

This paper derives the asymptotic distributions for a broad class of likelihood-based test statistics, unifying previous special cases and providing a general framework for statistical hypothesis testing.

Contribution

It introduces a comprehensive asymptotic formula for a general double-bounded custom-sided likelihood test statistic, extending prior specific results.

Findings

Unified asymptotic distribution formulas for likelihood-based tests

Special cases include previous test statistics by Cowan et al.

Provides theoretical foundation for future statistical analyses.

Abstract

This paper presents the asymptotic distributions of a general likelihood-based test statistic, derived using results of Wilks and Wald. The general form of the test statistic incorporates the test statistics and associated asymptotic formulae previously derived by Cowan, Cranmer, Gross and Vitells, which are seen to be special cases of the likelihood-based test statistic described here.