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

Author

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  • Jurgita Arnastauskaitė

    (Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania
    Department of Computer Sciences, 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)

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.

Suggested Citation

  • Jurgita Arnastauskaitė & Tomas Ruzgas & Mindaugas Bražėnas, 2021. "A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3003-:d:686149
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    References listed on IDEAS

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