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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Felipe Osorio & Manuel Galea & Claudio Henríquez & Reinaldo Arellano-Valle, 2023. "Addressing non-normality in multivariate analysis using the t-distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(4), pages 785-813, December.
    • Handle: RePEc:spr:alstar:v:107:y:2023:i:4:d:10.1007_s10182-022-00468-2
    DOI: 10.1007/s10182-022-00468-2
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