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Abstract:
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The problem of testing homogeneity of several multivariate normal mean vectors against an order restricted alternative hypothesis may arise in several situations. For example, in a proof-of-concept experiment evaluating the relationship between the dosage of a drug and outcome, where the outcome is multivariate in nature, investigators might be willing to assume that the mean responses on the outcome components are simultaneously non-decreasing (or non-increasing) functions of the dosage level. Sasabuchi (2003) derived a likelihood ratio-type test for homogeneity of ? 2 order-restricted mean vectors under a multivariate normality assumption with common covariance matrix. However, its null distribution depends on the unknown covariance matrix. In order to alleviate this difficulty, we propose a test that conditions on the sufficient statistic for the covariance matrix. This talk will discuss the derivation of the conditional test, demonstrate a method based on Markov Chain Monte Carlo sampling to calculate the p-value of the test, and illustrate the operating characteristics of the proposed test through simulation studies.
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