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Robust Likelihood Methods Based on the Skew‐t and Related Distributions


  • Adelchi Azzalini
  • Marc G. Genton


The robustness problem is tackled by adopting a parametric class of distributions flexible enough to match the behaviour of the observed data. In a variety of practical cases, one reasonable option is to consider distributions which include parameters to regulate their skewness and kurtosis. As a specific representative of this approach, the skew‐t distribution is explored in more detail and reasons are given to adopt this option as a sensible general‐purpose compromise between robustness and simplicity, both of treatment and of interpretation of the outcome. Some theoretical arguments, outcomes of a few simulation experiments and various wide‐ranging examples with real data are provided in support of the claim. Le problème de la robustesse est attaqué en adoptant une classe paramétrique de distributions qui sont suffisamment flexibles pour représenter le comportement des observations. Dans une variété de cas pratiques, une option raisonnable est de considérer des distributions qui incluent des paramètres pour régler leur asymétrie et leur aplatissement. Comme représentant spécifique de cette approche, la distribution t asymétrique est explorée plus en détail et des raisons sont apportées pour adopter cette option comme un compromis judicieux et à tous usages entre la robustesse et la simplicité du traitement et de l'interprétation des résultats. Quelques arguments théoriques, les résultats de simulations et divers exemples sur des données réelles sont fournis afin de soutenir cette affirmation.

Suggested Citation

  • Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
  • Handle: RePEc:bla:istatr:v:76:y:2008:i:1:p:106-129
    DOI: 10.1111/j.1751-5823.2007.00016.x

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