On Describing Multivariate Skewness: A Directional Approach
AbstractMost 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.
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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 0409010.
Length: 21 pages
Date of creation: 20 Sep 2004
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Note: Type of Document - pdf; pages: 21
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Bayesian methods; Multivariate distribution; Multivariate regression; Prior elicitation; Skewness.;
Find related papers by JEL classification:
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
- C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
- C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
- C5 - Mathematical and Quantitative Methods - - Econometric Modeling
- C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-09-30 (All new papers)
- NEP-ECM-2004-09-30 (Econometrics)
- NEP-ETS-2004-09-30 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
- Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
- Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
- Jose T.A.S. Ferreira & Mark F.J. Steel, 2004.
"Model Comparison of Coordinate-Free Multivariate Skewed Distributions with an Application to Stochastic Frontiers,"
- Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
- Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
- A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
- J.T.A.S. Ferreira & M.F.J. Steel, 2004.
"Modelling Directional Dispersion Through Hyperspherical Log- Splines,"
- José T. A. S. Ferreira & Mark F. J. Steel, 2005. "Modelling directional dispersion through hyperspherical log-splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 599-616.
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