1 - α Equivariant Confidence Rules for Convex Alternatives are α/2–Level Tests - With Applications to the Multivariate Assessment of Bioequivalence

Abstract

In general, a 1 — α confidence region C(X) for a parameter θ ∈ Θ yields a test at level a for H: θ ∈ Θ H versus K: θ ∈ ΘC H whenever we reject if C(X) ∪ ΘH = θ. We show under certain equivariance properties of C(X) that for the case of convex alternatives, ΘC H, the level of the resulting test is in fact α/2. This extends recent findings for hyperrectangular alternatives as they occur in the multivariate bioequivalence problem. Furthermore, we apply the suggested test to ellipsoid-type alternatives instead of hyperrectangulars in the multivariate bioequivalence problem and to a problem occurring in neurophysiology. Finally, we compare our test numerically with existing methods.