Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Rao-Robson Chi-Square Test for Multivariate Normality Based on the Mahalanobis Distances

  • Park, Cheolyong (Associate Professor, Department of Statistics, Keimyung University)
  • Published : 2000.08.01
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Abstract

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

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References

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