Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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The Limit Distribution of an Invariant Test Statistic for Multivariate Normality

  • Kim Namhyun (Department of Science, Hongik University)
  • Published : 2005.04.01
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Abstract

Testing for normality has always been an important part of statistical methodology. In this paper a test statistic for multivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process.

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