Abstract
We propose a practical method to test the hypothesis of multivariate normality. The multivariate normal distribution is characterized by the fact that all its joint cumulants of order higher than two are zero, so that a simple and natural way to test the hypothesis of multivariate normality will be to use sample cumulants as test statistics. In view of this, we suggest to compute exact conditional moments of sample cumlants given sample variances and covariances. And by applying asymptotic normality, we calculate exact second order conditional moments of the third cumulants, which will be used to test the normality.
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References
Markovich, J.F. & Afifi, A.A. (1973). On Test for Multivariate Normality, Journal of American Statistical Association 68, 176–179.
Kendall, M.G. & Stuart, A. (1958) Advanced Theory of Statistics, 2nd ed. Griffin.
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Takeuchi, K. A Test for Multivariate Normality. Behaviormetrika 1, 59–64 (1974). https://doi.org/10.2333/bhmk.1.59
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DOI: https://doi.org/10.2333/bhmk.1.59