Sub-dimensional Mardia measures of multivariate skewness and kurtosis

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dc.contributor.authorChowdhury, Joydeep
dc.contributor.authorDutta, Subhajit
dc.contributor.authorArellano-Valle, Reinaldo B.
dc.contributor.authorGenton, Marc G.
dc.date.accessioned2025-01-20T21:01:32Z
dc.date.available2025-01-20T21:01:32Z
dc.date.issued2022
dc.description.abstractThe Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these mea-sures do not reflect the sub-dimensional features of the distribution. Consequently, test-ing procedures based on these measures may fail to detect skewness or kurtosis present in a sub-dimension of the multivariate distribution. We introduce sub-dimensional Mar-dia measures of multivariate skewness and kurtosis, and investigate the information they convey about all sub-dimensional distributions of some symmetric and skewed families of multivariate distributions. The maxima of the sub-dimensional Mardia measures of multivariate skewness and kurtosis are considered, as these reflect the maximum skewness and kurtosis present in the distribution, and also allow us to identify the sub-dimension bearing the highest skewness and kurtosis. Asymptotic distributions of the vectors of sub-dimensional Mardia measures of multivariate skewness and kurtosis are derived, based on which testing procedures for the presence of skewness and of deviation from Gaussian kurtosis are developed. The performances of these tests are compared with some existing tests in the literature on simulated and real datasets. (c) 2022 Elsevier Inc. All rights reserved.
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.jmva.2022.105089
dc.identifier.issn0047-259X
dc.identifier.urihttps://doi.org/10.1016/j.jmva.2022.105089
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/92906
dc.identifier.wosidWOS:000879232000004
dc.language.isoen
dc.revistaJournal of multivariate analysis
dc.rightsacceso restringido
dc.subjectAsymptotic distribution
dc.subjectMultivariate normality test
dc.subjectSkew-normal distribution
dc.subjectSkew-t distribution
dc.subjectSymmetric distribution
dc.subjectMeasures of multivariate skewness and kurtosis
dc.subject.ods03 Good Health and Well-being
dc.subject.odspa03 Salud y bienestar
dc.titleSub-dimensional Mardia measures of multivariate skewness and kurtosis
dc.typeartículo
dc.volumen192
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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