Some implications of the union-intersection principle for tests of sphericity

W. Venables

Journal of Multivariate Analysis, 1976, vol. 6, issue 1, 185-190

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.

Keywords: Sphericity; tests; independence; tests; union-intersection; principle (search for similar items in EconPapers)
Date: 1976
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