Some implications of the union-intersection principle for tests of sphericity |
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Authors: | W Venables |
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Institution: | Department of Statistics, University of Adelaide Australia |
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Abstract: | The sphericity hypothesis may be expressed as an intersection of simpler hypotheses on the invariant subspaces of the variance matrix. Applying the union-intersection principle to dissections of this type establishes a link between tests of independence and tests of sphericity. We use some recent results of Bloomfield and Watson 2] and Knott 4] to derive a class of union-intersection tests for sphericity from likelihood ratio tests of independence of two sets of variates. As well, we show that the ordinary likelihood ratio test for sphericity has a natural union-intersection interpretation. |
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Keywords: | 62H15 62F05 Sphericity tests independence tests union-intersection principle |
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