Simultaneous inference of correlated marginal tests using intersection-union or union-intersection test principle

Two main approaches in simultaneous inference are intersection-union tests and union-intersection tests. For intersection-union hypotheses, the classical IUT based on marginal p-values and the all-in-alternative UIT are compared. Depending on correlation, number of marginal tests and patterns of the alternative the inherent power loss of the aiaUIT seems to be acceptable, considering its advantage, namely the availability of simple-to-interpret simultaneous confidence interval.