Title: Objective Bayesian analysis of the multivariate regression model with skew-$t$ errors
Authors: Antonio Parisi - University of Rome Tor Vergata (Italy) [presenting]
Brunero Liseo - Sapienza Universita di Roma (Italy)
Abstract: In the last decades, several specifications of skew-Student $t$ distributions have been proposed as empirical models for data characterized by skewness and/or extra-kurtosis. The flexibility provided by these models generally comes at the cost of several inferential difficulties, mostly in the multivariate setup. Under a Bayesian perspective, we consider a (possibly multivariate) regression model in which the error vector term has a multivariate skew-elliptical distribution. More specifically, a skew-$t$ distribution or a special case of it: the Student-$t$, the skew-normal or the Gaussian distribution. For this regression model, we propose a set of objective priors and a specifically designed Monte Carlo sampler. The new version of the R package mvst contains functions that implement the described methods, in particular to estimate the model and to obtain pseudo-random draws. The package also allows the choice among the skew-$t$ model and the nested ones via the Bayes factor. Moreover, it allows to generalize the reference model in several ways; as an example, a stochastic frontier model can be estimated by a change in the elicitation of the prior distribution for the shape parameter.