An overall test for multivariate normality

Rao, C. R. ; Ali, Hydar (1997) An overall test for multivariate normality Student, 2 . pp. 317-324. ISSN 0039-2685

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There are a number of methods in the statistical literature for testing whether observed data came from a multivariate normal(MVN) distribution with an unknown mean vector and covariance matrix. Let X1, ...,Xn be an iid sample of size n from a p-variate normal distribution. Denote the sample mean and sample variance-covariance matrix by X̅ and S respectively. Most of the tests of multivariate normality are based on the results that Yi=S(Xi-X̅), i=1,..., n, are asymptotically iid as p-variate normal than zero mean vector and identity covariance matrix. Tests developed by Andrews et al., Mardina and others are direct functions of Yi. We note that the N=np components of the Yi's put together can be considered as an asymptotically iid sample of size N from a univariate normal any well known test based on N independent observations for univariate normality. In Particular we can use univariate skewness and kurtosis tests, which are sensitive to deviations from normality.

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Deposited On:28 Nov 2011 04:20
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