A Modified Normalizing Transformation Statistic Based on Kurtosis Testing Multivariate Normality

In this paper, we consider a testing problem of multivariate normality (MVN). We deal with the kurtosis test statistic based on Mardia's multivariate kurtosis as an MVN test and propose a modified normalizing transformation (NT) statistic. The accuracy of the normal approximation of the proposed test statistic through a Monte Carlo simulation is investigated. The results of empirical power of a modified NT statistic are presented. Alternative distributions are chosen to represent different types of departure from multivariate normality. Moreover, to compare the empirical power of the modified NT statistic, we target a NT statistic, the improved Mardia's test statistic, and the Henzer-Zirkler test statistic. Finally, an example is provided.