Testing non-oblique hypotheses

This paper considers a likelihood ratio test for testing hypotheses defined by non-oblique closed convex cones, satisfying the so called iteration projection property, in a set of k normal means. We obtain the critical values of the test using the Chi-Bar-Squared distribution. The obtuse cones are introduced as a particular class of cones which are non-oblique with every one of their faces. Examples with the simple tree order cone and the total order cone are given to illustrate the results.