, Volume 35, Issue 1, pp 339–348 | Cite as

A consistent test for multivariate normality based on the empirical characteristic function

  • L. Baringhaus
  • N. Henze


LetX 1,X 2, …,X n be independent identically distributed random vectors in IR d ,d ⩾ 1, with sample mean\(\bar X_n \) and sample covariance matrixS n. We present a practicable and consistent test for the composite hypothesisH d: the law ofX 1 is a non-degenerate normal distribution, based on a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residualsS n −1/2 (X j\(\bar X_n \)) and its pointwise limit exp (−1/2|t|2) underH d. The limiting null distribution of the test statistic is obtained, and a table with critical values for various choices ofn andd based on extensive simulations is supplied.


Null Distribution Multivariate Normality Consistent Test Epps Composite Hypothesis 
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Copyright information

© Physica-Verlag Ges.m.b.H 1988

Authors and Affiliations

  • L. Baringhaus
    • 1
  • N. Henze
    • 1
  1. 1.Institut für Mathematische StochastikUniversität HannoverHannover 1FRG

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