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

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.