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Testing the significance of the RV coefficient

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  • Josse, J.
  • Pagès, J.
  • Husson, F.

Abstract

The relationship between two sets of variables defined for the same individuals can be evaluated by the RV coefficient. However, it is impossible to assess by the RV value alone whether or not the two sets of variables are significantly correlated, which is why a test is required. Asymptotic tests do exist but fail in many situations, hence the interest in permutation tests. However, the main drawbacks of the permutation tests are that they are time consuming. It is therefore interesting to approximate the permutation distribution with continuous distributions (without doing any permutation). The current approximations (normal approximation, a log-transformation and Pearson type III approximation) are discussed and a new one is described: an Edgeworth expansion. Finally, these different approximations are compared for both simulations and for a sensory example.

Suggested Citation

  • Josse, J. & Pagès, J. & Husson, F., 2008. "Testing the significance of the RV coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 82-91, September.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:82-91
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    References listed on IDEAS

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    1. Kazi-Aoual, Frederique & Hitier, Simon & Sabatier, Robert & Lebreton, Jean-Dominique, 1995. "Refined approximations to permutation tests for multivariate inference," Computational Statistics & Data Analysis, Elsevier, vol. 20(6), pages 643-656, December.
    2. Booth, J. G. & Hall, P. & Wood, A. T. A., 1994. "On the Validity of Edgeworth and Saddlepoint Approximations," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 121-138, October.
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    4. Robert, P. & Cleroux, R. & Ranger, N., 1985. "Some results on vector correlation," Computational Statistics & Data Analysis, Elsevier, vol. 3(1), pages 25-32, May.
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    12. Mayer Claus-Dieter & Lorent Julie & Horgan Graham W, 2011. "Exploratory Analysis of Multiple Omics Datasets Using the Adjusted RV Coefficient," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, March.
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