Abstract
We consider testing the equality of vector means against a multivariate ordered alternative. An extension of the Abelson and Tukey test is first derived under the assumption that the covariance matrix is known. The asymptotic distribution is obtained when the covariance is estimated. We also extend Schaafsma and Smid's somewhere most powerful test to multivariate normal settings, under the assumption that the covariance matrix is known. An empirical power study shows that these tests perform better than their multi-sided χ2 test counterparts.
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