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Title: The simultaneous test of equality and circularity of several covariance matrices Authors:  Filipe Marques - Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, FCT, NOVA University of Lisbon (Portugal) [presenting]
Carlos Coelho - NOVA University of Lisbon (Portugal)
Abstract: The simultaneously test of equality and circularity of several covariance matrices is studied, and accurate near-exact approximations are developed for the distribution of the associated likelihood ratio test statistic. The equality of covariance matrices test is widely used in many statistical procedures and, recently, matrices with a circular pattern, which are particular cases of the well known Toeplitz matrices, have been considered in many practical applications. Therefore a statistical procedure which may allow to test simultaneously both the equality and circularity of a given number of covariance matrices may be a powerful and useful practical tool. Based on a decomposition of the null hypothesis in study, which induces a convenient factorization on the likelihood ratio test statistic, the authors show how it is possible to derive precise and easy to implement near-exact approximations for the distribution of the likelihood ratio test statistic. Numerical studies are carried out to assess the quality of these approximations and to study the properties of this test.