A multivariate analogue of the one-sided test

In this paper we consider the following problem. Given a multivariate normal population with known variance matrix, what test is appropriate to determine whether the means are slipped to the right? In the case when the population is univariate normal, this problem can be solved by the ordinary one-sided test using either the normal or the t-distribution functions. It is the purpose of this paper to develop what may be termed a multivariate analogue of the one-sided test of significance.

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