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

@article{Baringhaus1988ACT,
  title={A consistent test for multivariate normality based on the empirical characteristic function},
  author={Ludwig Baringhaus and Norbert Henze},
  journal={Metrika},
  year={1988},
  volume={35},
  pages={339-348}
}
AbstractLetX1,X2, …,Xn be independent identically distributed random vectors in IRd,d ⩾ 1, with sample mean $$\bar X_n $$ and sample covariance matrixSn. We present a practicable and consistent test for the composite hypothesisHd: the law ofX1 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 residualsSn−1/2(Xj − $$\bar X_n $$ ) and its pointwise limit exp (−1/2|t|2) underHd. The… 

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