Multivariate skewing mechanisms: a unified perspective based on the transformation approach

Christophe Ley (1) , Davy Paindaveine (1)

1 ULB - Département d'Informatique [Bruxelles]

In recent years, models for (possibly multivariate) skewed distributions have become more and more popular. In the univariate case, Ferreira and Steel (2006) [Ferreira, J.T.A.S., Steel, M.F.J., 2006. A constructive representation of univariate skewed distributions. J. Amer. Statist. Assoc. 101, 823-829] introduced general skewing mechanisms in order to compare existing skewing methods in a common framework and to ease construction of new such methods according to the needs in given situations. In this paper, we make use of the classical transformation approach to define alternative skewing mechanisms for the same purpose. While keeping all nice features of Ferreira and Steel's skewing mechanisms (flexibility, surjectivity, possibility of retaining prespecified characteristics of the original symmetric distribution, etc.), our skewing mechanisms, unlike theirs, can easily be extended to the multivariate case. We describe our skewing schemes, investigate their main properties, and illustrate their effects on standard (multi)normal distributions by means of a few examples. Finally, we briefly discuss their relevance in the context of optimal symmetry testing.

Mots clés: 60E05; 62H05; 62E10; Probability transform; Skewing mechanism; Skew-normal distribution; Sinh-arcsinh transform; Tail behavior; Transformation approach

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Christophe Ley, Davy Paindaveine. Multivariate skewing mechanisms: a unified perspective based on the transformation approach. Statistics and Probability Letters, 2010, 80 (23-24), pp.1685. ⟨10.1016/j.spl.2010.07.004⟩. ⟨hal-00691790⟩