Likelihood-Ratio and Confidence-Region Tests

Abstract

A previous paper (Aitchison, 1964) proposed a method of confidence-region testing for multiple-hypothesis situations and developed the theory for linear univariate situations and for the asymptotic parametric case. The present paper shows that the results for these situations are in fact special cases of a basic relation between confidence-region tests and likelihood-ratio tests. This relation allows the easy extension of confidence-region testing to multivariate analysis.