Communications for Statistical Applications and Methods

  • 제12권1호
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  • Pages.71-86
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  • 2005
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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The Limit Distribution of an Invariant Test Statistic for Multivariate Normality

  • Kim Namhyun (Department of Science, Hongik University)
  • 발행 : 2005.04.01
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초록

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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참고문헌

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피인용 문헌

  1. Tests Based on Skewness and Kurtosis for Multivariate Normality vol.22, pp.4, 2015, https://doi.org/10.5351/CSAM.2015.22.4.361