1-alpha equivariant confidence rules for convex alternatives are alpha/2-level tests - With applications to the multivariate assessment of bioequivalence

Abstract

In general, a 1 - alpha confidence region C(X) for a parameter theta epsilon - yields a test at level alpha for H: theta epsilon -(H) versus K: theta epsilon -(C)(H) whenever we reject if C(X) boolean AND -(H) = 0. We show under certain equivariance properties of C(X) that for the case of convex alternatives, 0(H)(C), the level of the resulting test is in fact alpha/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.