Abstract: This paper studies the invariant structure of the one-sided testing problem μ=0 vs μ>=0 in Np(μ,Σ) and it is shown that the requirement of scale invariance, symmetry in coordinates and similarity (transitivity) inevitably leads to the Hotelling T 2 test. We regard this as a negative result in the following sense: Since we cannot recommend Hotelling T&nbs p;2 test for this one-sided problem it is fruitless to seek an invariant-similar test for this problem.
In addition to the above result, a noncentral bivariate t-di stribution is derived, a different invariance approach is proposed when similarity is not obtained though the usual invariance approach, and the non-Bayes property of the Hotelling T 2 test is shown.
Key words and phrases: One-sided testing problem, bivariate t distribution, scale invariance, permutation invariance, similar test, Hotelling T 2.