Testing for multivariate normality based on generalization of empirical distribution function†
Namhyun Kim1
1Department of Science, Hongik University
Correspondence to: † This work was supported by 2023 Hongik University Research Fund.
1 Professor, Department of Science, Hongik University, Seoul 04066, Korea. E-mail: nhkim@hongik.ac.kr
1 Professor, Department of Science, Hongik University, Seoul 04066, Korea. E-mail: nhkim@hongik.ac.kr
Received February 22, 2024; Revised March 16, 2024; Accepted March 18, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- Testing multivariate normality is a topic of ongoing practical and theoretical interest in statistical inference. We generalize goodness-of-fit test statistics based on the empirical distribution function to test multivariate normality. Kesmen et al. (2021) defined a multivariate empirical distribution function and generalized the Kolmogorov-Smirnov statistic to multivariate cases. In this paper the Cramér-von Mises statistic and the Anderson-Darling statistic are generalized by the same way. Through simulation study, the Anderson-Darling statistic showed the best power among three of them. Since the statistics run very simply even in multivariate cases, they could be easily applied in practical situation.
- Keywords : Empirical distribution function, goodness-of-fit tests, multivariate normality
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