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

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 covar...

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Bibliographic Details
Published in:Advances in statistical analysis : AStA : a journal of the German Statistical Society 2023-12, Vol.107 (4), p.785-813
Main Authors: Osorio, Felipe, Galea, Manuel, Henríquez, Claudio, Arellano-Valle, Reinaldo
Format: Article
Language:English
Subjects:
Covariance matrix
Econometrics
Economics
Finance
Insurance
Management
Mathematics and Statistics
Multivariate analysis
Original Paper
Performance evaluation
Probability Theory and Stochastic Processes
Statistics
Statistics for Business
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Summary: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.
ISSN:1863-8171
1863-818X
DOI:10.1007/s10182-022-00468-2