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Abstract
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Consider the problem of testing the isotonic of several p-variate normal mean
vectors against all alternatives. It is difficult to compute the exact p-value for
this problem of testing with the classical method when the covariance matrices
are completely unknown. In the present paper, a test statistic is proposed for this
problem of testing. A reformulation of the test statistic is given based on the
orthogonal projections on the closed convex cones and then the upper bound for
p-value of the test statistic is computed.
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