Comparative analysis of some approaches to multivariate normality test

Abstract

Many common multivariate statistical techniques rely on the assumption of multivariate normality (MVN), but this assumption can often be violated in real-world data. To assess whether data deviate from MVN, various tests have been developed, including ones that use multivariate concepts like the "standardized distance method," "Mardia skewness," and "Mardia kurtosis." In this study, Monte Carlo simulations were employed to generate synthetic data to compare these three methods. Test statistics were computed for each method and then compared to the appropriate asymptotic critical values. The outcomes, indicating whether the null hypothesis was accepted or rejected in each case, were recorded and analyzed. From the result of analysis, multivariate normality was accepted at ????=0.05 level using Standardized Distance Test and Mardia Skewness, on the other hand, Mardia Kurtosis rejected MVN at ????=0.05 for the simulated data which is the most effective method out of the three procedures used in this work.