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

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  • Venables, W.

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.

Suggested Citation

  • Venables, W., 1976. "Some implications of the union-intersection principle for tests of sphericity," Journal of Multivariate Analysis, Elsevier, vol. 6(1), pages 185-190, March.
    • Handle: RePEc:eee:jmvana:v:6:y:1976:i:1:p:185-190
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    Cited by:

    1. Dotelli, G. & Jansen, L., 1996. "On the crystal structure problem for heavy rare-gas solids: A three-atom exchange perturbation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 234(1), pages 151-166.

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