Addressing non-normality in multivariate analysis using the t-distribution

Felipe Osorio (), Manuel Galea (), Claudio Henríquez () and Reinaldo Arellano-Valle ()
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Felipe Osorio: Universidad Técnica Federico Santa María
Manuel Galea: Pontificia Universidad Católica de Chile
Claudio Henríquez: Pontificia Universidad Católica de Chile
Reinaldo Arellano-Valle: Pontificia Universidad Católica de Chile

AStA Advances in Statistical Analysis, 2023, vol. 107, issue 4, No 8, 785-813

Abstract: Abstract The main aim of this paper is to propose a set of tools for assessing non-normality taking into consideration the class of multivariate t-distributions. Assuming second moment existence, we consider a reparameterized version of the usual t distribution, so that the scale matrix coincides with covariance matrix of the distribution. We use the local influence procedure and the Kullback–Leibler divergence measure to propose quantitative methods to evaluate deviations from the normality assumption. In addition, the possible non-normality due to the presence of both skewness and heavy tails is also explored. Our findings based on two real datasets are complemented by a simulation study to evaluate the performance of the proposed methodology on finite samples.

Keywords: Kullback–Leibler divergence; Local influence; Negentropy; Outliers (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:alstar:v:107:y:2023:i:4:d:10.1007_s10182-022-00468-2

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DOI: 10.1007/s10182-022-00468-2

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