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

ABSTRACT

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.

KEYWORDS:

• BHEP tests
• Monte Carlo power comparison
• Multiple testing
• Tests for multivariate normality

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G10
• 62H15

Acknowledgments

The author expresses his thanks to Professor Norbert Henze who has suggested replacing the Mardia tests used in the MB multiple test by the extreme BHEP statistics, and to the reviewers for their comments and suggestions.

Funding

This research was partially supported by the Centro de Matemática da Universidade de Coimbra (funded by the European Regional Development Fund through the program COMPETE and by the Portuguese Government through the FCT–Fundação para a Ciência e Tecnologia under the project PEst-C/MAT/UI0324/2011).