# 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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