A New Jarque-Bera Type Omnibus Goodness-of-fit Test for Multivariate Normality
Mbanefo S. Madukaife *
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a new Jarque-Bera type statistic for assessing the multivariate normality of a multivariate datasets is obtained. The affine-invariant and consistent statistic is shown to follow, asymptotically, a chi-square distribution with 2 degrees of freedom. The critical values of the test were evaluated empirically through extensive simulation studies for different sample sizes and different random vector dimensions. Also, the empirical type-I-error rates and empirical powers of the proposed test were compared with some other well-known competing statistics in the literature. The results obtained showed that the proposed omnibus statistic is a powerful tool for assessing multivariate normality (MVN) of multivariate datasets.
Keywords: Asymptotic null distribution, empirical critical values, omnibus test, skewness and kurtosis measures, test for multinormality