New Hypotheses and Tests for the Multivariate Bioequivalence Problem

Testing for the bioequivalence alternative H₁: |θ| ≤ Δ in a normal univariate setting is usually performed with the well-known ”two-one-sidedt-tests procedure”, which is an intersection-union test. Based on the intersection-union principle recently tests for the multivariate rectangular alternative H _d : max _i = 1,..., d |θ _i | ≤ Δ have been constructed. In this paper we show that rectangular hypotheses are not always a suitable generalization of H₁ to the multivariate setting. In order to overcome the drawbacks encountered with rectangular hypotheses we suggest ellipsoids as alternatives. Finally, an asymptotic test for the new hypotheses is suggested and compared with existing methods.