1-alpha equivariant confidence rules for convex alternatives are alpha/2-level tests - With applications to the multivariate assessment of bioequivalence
A. Munk et R. Pfluger, 1-alpha equivariant confidence rules for convex alternatives are alpha/2-level tests - With applications to the multivariate assessment of bioequivalence, J AM STAT A, 94(448), 1999, pp. 1311-1319
In general, a 1 - alpha confidence region C(X) for a parameter theta epsilo
n - 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 un
der certain equivariance properties of C(X) that for the case of convex alt
ernatives, 0(H)(C), the level of the resulting test is in fact alpha/2. Thi
s extends recent findings for hyperrectangular alternatives as they occur i
n the multivariate bioequivalence problem. Furthermore, we apply the sugges
ted test to ellipsoid-type alternatives instead of hyperrectangulars in the
multivariate bioequivalence problem and to a problem occurring in neurophy
siology. Finally, we compare our:test numerically with existing methods.