Normal Scores in Tests of Independence

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Other Title
  • 正規スコアと独立性検定
  • オボエガキ セイキ スコア ト ドクリツセイ ケンテイ

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When applying a multivariate statistical method based on the normality assumption to non-normal data, one is tempted to use normal scores for those variates which are apparently non-normal. However, even if all marginal distributions are normal, the joint distribution is not necessarily normal and the method may fail. As a simple counter example, a degenerate bivariate copula which is symmetric about the y-axis, and its normal transformation, the Degenerated Uncorrelated Marginally Normal (DUMgN) distribution, are introduced. Pearson correlation tests of samples from the DUMgN are simulated, and the power of the test is shown to be too poor to be useful. Two other distributions, which are symmetric about both the x and y axes, one is degenerate and the other non-degenerate, are used to further demonstrate the poor performance.

Journal

  • Ouyou toukeigaku

    Ouyou toukeigaku 34 (2), 121-138, 2005

    Japanese Society of Applied Statistics

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