MULTIVARIATE TESTS OF NORMAL MEAN VECTORS WITH RESTRICTED ALTERNATIVES

ABSTRACT In this paper, we consider tests for the hypothesis that the mean vector is zero against one-sided alternatives when the observation vectors are independently and identically distributed as normal with unknown covariance matrix. The exact null-distribution of the tests is derived. The tests generalize the centre-direction test proposed by Tang et al.[1] for known covariance. In addition, the modification is order- and scale-invariant. Power comparisons with some other tests are presented. It can be shown that the null distribution of the test statistic holds for data arising from any elliptical distribution, not just the normal distribution.

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