Equivalence of likelihood ratio tests and obliquity

This paper shows how in a normal population, when the mean holds restrictions given by a right cone, the likelihood ratio test (LRT) for testing a face of that cone is equivalent to another test which is also the LRT for testing the linear subspace associated to the above face against a right cone defined only by those restrictions taking part in the definition of the subspace. Obliqueness is introduced and the equivalence with strict acuteness of a cone is proved, becoming useful to explain the dominance or equivalence of the LRT for testing a face of a cone.