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Abstract:
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We introduce two new families of non-parametric tests of goodness of fit on the classical groups. One of them is a family of tests for the eigenvalue distribution of the Haar measure, which is consistent against all fixed alternatives. This extends a family of similar tests on the unitary group, introduced by [Coram and Diaconis, 2003], to the other classical groups. The other is a family of tests for the full Haar measure, which is consistent against all fixed alternatives. We find the asymptotic distribution under the null and general alternatives. This allows for derivation of formulas for the local power against particular parametric families. We apply our tests to different synthetic and real data sets on the orthogonal group.
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