On Describing Multivariate Skewness: A Directional Approach

Jose Ferreira () and Mark Steel

Econometrics from University Library of Munich, Germany

Abstract: Most multivariate measures of skewness in the literature measure the overall skewness of a distribution. While these measures are perfectly adequate for testing the hypothesis of distributional symmetry, their relevance for describing skewed distributions is less obvious. In this article, we consider the problem of characterising the skewness of multivariate distributions. We define directional skewness as the skewness along a direction and analyse parametric classes of skewed distributions using measures based on directional skewness. The analysis brings further insight into the classes, allowing for a more informed selection of particular classes for particular applications. In the context of Bayesian linear regression under skewed error we use the concept of directional skewness twice. First in the elicitation of a prior on the parameters of the error distribution, and then in the analysis of the skewness of the posterior distribution of the regression residuals.

Keywords: Bayesian methods; Multivariate distribution; Multivariate regression; Prior elicitation; Skewness. (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2004-09-20
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: Type of Document - pdf; pages: 21
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0409010

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