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On Describing Multivariate Skewness: A Directional Approach

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Author Info

  • J. T. A. S. Ferreira

    (University of Warwick)

  • M. F. J. Steel

    (University of Warwick)

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.

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File URL: http://128.118.178.162/eps/em/papers/0409/0409010.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0409010.

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Length: 21 pages
Date of creation: 20 Sep 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0409010

Note: Type of Document - pdf; pages: 21
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Web page: http://128.118.178.162

Related research

Keywords: Bayesian methods; Multivariate distribution; Multivariate regression; Prior elicitation; Skewness.;

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References

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  1. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Model Comparison of Coordinate-Free Multivariate Skewed Distributions with an Application to Stochastic Frontiers," Econometrics, EconWPA 0404005, EconWPA.
  2. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
  3. 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.
  4. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
  5. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics, EconWPA 0403001, EconWPA.
  6. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper, Tilburg University, Center for Economic Research 1996-58, Tilburg University, Center for Economic Research.
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Cited by:
  1. 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.
  2. Alexios Ghalanos & Eduardo Rossi & Giovanni Urga, 2012. "Independent Factor Autoregressive Conditional Density Model," DEM Working Papers Series 021, University of Pavia, Department of Economics and Management.

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