© Grzegorz Kończak. Article available under the CC BY-SA 4.0 licence
ARTICLE
ABSTRACT
The article presents a proposal for a goodness-of-fit test for multivariate normality. The idea of the test is based on the empty cells test, which is well known in the literature. In the empty cells test, the area of the random variable's variability is divided into m disjoint cells. Assuming the truth of hypothesis H0, which proclaims the multivariate normality of the distribution with given parameters, disjoint cells are arranged in such a way that random values with equal probabilities are in each cell. Based on the n-element sample, the number of empty cells, i.e. the cells without any elements from the sample, is determined. Crucial to the proposed procedure is the division of the multidimensional area of variation into disjoint cells. The advantage of this test is that it can be used for relatively small samples. In the article, a simulation comparison of the proposed test's properties and the Kolmogorov-Smirnov test's multivariate version is carried out.
KEYWORDS
multivariate normality, inferential statistics, empty cells test, Monte Carlo study
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