When dealing with normal random variables, one can test a hypothesis regarding the parameter of the expected value. Often, a one-tailed test is used. However, in the case of multivariate normal distributions, this concept becomes unclear. The thesis focuses on a "one-sided" test with an alternative in the positive orthant. The "new" test is a modification of the standard likelihood ratio test. Its power and significance level are justified by a theorem and its corollary. Through simulation, we further confirm that the test's power for expected values in the positive orthant is greater than that of the standard likelihood ratio test.
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