# 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}
}
• Published 1 December 1988
• Mathematics
• Metrika
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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