On the Power Behaviour of Läuter's Exact Multivariate One‐sided Tests

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Abstract
Recently Läuter [1996] developed a new class of parametric tests for the one‐sided multivariate hypothesis with unknown covariances. Unlike most procedures for this problem, Läuter's tests are exact, i.e. they strictly maintain the nominal level. In this paper two scale invariant Läuter tests are considered, the standardized sum and the principal component test. Here conditions are investigated under which the powers of these tests are insufficient for arbitrarily large alternatives and, for the second test, also for unbounded sample sizes. It turns out that power insufficiencies can happen only at the boundary of the set of alternatives so that for alternatives usually occurring in biometrical practice both tests prove to be efficient.