Maximal Invariants Over Symmetric Cones

Details Maximal Invariants Over Symmetric Cones Maximal Invariants Over Symmetric Cones

2012-01-02

arxiv.org/abs/1201.0514v1

Mathematics

Statistics Theory

19 pages

Scientific paper

In this paper we consider some hypothesis tests within a family of Wishart distributions, where both the sample space and the parameter space are symmetric cones. For such testing problems, we first derive the joint density of the ordered eigenvalues of the generalized Wishart distribution and propose a test statistic analog to that of classical multivariate statistics for testing homoscedasticity of covariance matrix. In this generalization of Bartlett's test for equality of variances to hypotheses of real, complex, quaternion, Lorentz and octonion types of covariance structures.

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