Study of multivariate asymmetric distributions using univariate two-piece distributions

When analyzing data, among the most important questions is which distribution does appropriately describe the probabilistic model that is behind the data. In the simplest univariate setting, one of the first questions to ask is whether the distribution is symmetric, skewed to the right, the left, heavy tailed, light tailed etc. In recent years some interesting (large) parametric families of asymmetric densities have been studied. This recent work opens new and interesting gateways for distributional theory, and complement some major approaches to construct skew distributions from symmetric distributions. Of particular interest when studying distributions is not only their skewness but also whether their tails are such that they allow for dealing appropriately with the modelling of extremal events. Speaking in quantile terms, this means that one would be interested in particular in quantiles of orders close to one (in the extreme right-hand tail) or zero (in the extreme left-hand tail). Recent studies of the asymmetric families of distributions restrict to fixed orders staying away from zero and one.

A first main question that will be looked upon is how the recently studied families of asymmetric distributions can deal with inference for extreme quantiles, or (in the regression setting) with extreme regression quantiles. In many applications, for example in financial and actuarial applications and  in environmental sciences, the study of (extreme) regression quantiles is of importance.

Working in a fully parametric framework is often too restrictive, since the stringent model assumptions cannot be justified/motivated. Hence another aspect of the above problem, is to bring in model flexibility.

This can be done by bringing in semiparametric and nonparametric elements in the modelling. In a regression setting an additional challenge is to deal with the high-dimensionality of the problem, and eventually also to deal with model and/or variable selection aspects.

In the work interest will go beyond the simple univariate setting. Some examples, the analysis of multivariate data requires the study of multivariate asymmetric distributions and  analysis of circular data requests for a separate study of appropriate asymmetric distributions.