B0539
Title: Hypothesis test of a block compound symmetric covariance matrix for two-level multivariate data
Authors: Anuradha Roy - The University of Texas at San Antonio (United States) [presenting]
Carlos Coelho - NOVA University of Lisbon, NOVA-Math and NOVA.id.FCT (Portugal)
Abstract: The purpose is to study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the use of a suitable block-diagonalization of the hypothesis matrix, it is possible to obtain a decomposition of the main hypothesis into two sub-hypotheses. By using this decomposition it is then possible to obtain the likelihood ratio test statistic as well as its exact moments in a much simpler way. The exact distribution of the likelihood ratio test statistic is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes. A real data example is presented and a simulation study is also conducted.
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