EconPapers    
Economics at your fingertips  
 

Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions

Jose Tome Ferreira () and Mark Steel ()

Econometrics from EconWPA

Abstract: In this paper, we introduce a novel class of skewed multivariate distributions and, more generally, a method of building such a class on the basis of univariate skewed distributions. The method is based on a general linear transformation of a multidimensional random variable with independent components, each with a skewed distribution. Our proposed class of multivariate skewed distributions has a simple, intuitive form for the pdf, moment existence only depends on the existence of the moments of the underlying symmetric univariate distributions, and we avoid any conditioning on unobserved variables. In addition, we can freely allow for any mean and covariance structure in combination with any magnitude and direction of skewness. In order to deal with both skewness and fat tails, we introduce multivariate skewed regression models with fat tails, based on Student distributions. We present two main classes of such distributions, one of which is novel even under symmetry. Under standard non-informative priors on both regression and scale parameters, we derive conditions for propriety of the posterior and for existence of posterior moments. We describe MCMC samplers for conducting Bayesian inference and analyse two applications, one concerning the distribution of various measures of firm size and another on a set of biomedical data.

Keywords: Asymmetric distributions; Heavy tails; Linear regression model; Mardia's measure of skewness; Orthogonal matrices; Posterior propriety. (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2004-03-04
Note: Type of Document - pdf; prepared on WinXp; pages: 29
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (10) Track citations by RSS feed

Downloads: (external link)
http://128.118.178.162/eps/em/papers/0403/0403001.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:wpa:wuwpem:0403001

Access Statistics for this paper

More papers in Econometrics from EconWPA
Series data maintained by EconWPA ().

 
Page updated 2014-07-20
Handle: RePEc:wpa:wuwpem:0403001