A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study

Jurgita Arnastauskaitė, Tomas Ruzgas and Mindaugas Bražėnas
Additional contact information
Jurgita Arnastauskaitė: Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania
Tomas Ruzgas: Department of Computer Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania
Mindaugas Bražėnas: Department of Mathematical Modelling, Kaunas University of Technology, 51368 Kaunas, Lithuania

Mathematics, 2021, vol. 9, issue 23, 1-20

Abstract: The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

Keywords: multivariate normality; power of tests; squared radii; skewness; kurtosis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/23/3003/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/23/3003/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:23:p:3003-:d:686149

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().