A new test for multivariate normality by combining extreme and nonextreme BHEP tests

In this article, we propose a new multiple test procedure for assessing multivariate normality, which combines BHEP (Baringhaus–Henze–Epps–Pulley) tests by considering extreme and nonextreme choices of the tuning parameter in the definition of the BHEP test statistic. Monte Carlo power comparisons indicate that the new test presents a reasonable power against a wide range of alternative distributions, showing itself to be competitive against the most recommended procedures for testing a multivariate hypothesis of normality. We further illustrate the use of the new test for the Fisher Iris dataset.