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Modelling Directional Dispersion Through Hyperspherical Log- Splines

Author

Listed:
  • J.T.A.S. Ferreira

    (University of Warwick)

  • M.F.J. Steel

    (University of Warwick)

Abstract

We introduce the directionally dispersed class of multivariate distributions, a generalisation of the elliptical class. By allowing dispersion of multivariate random variables to vary with direction it is possible to generate a very wide and flexible class of distributions. Directionally dispersed distributions are shown to have a simple form for their density, which extends a spherically symmetric density function by including a function D modelling directional dispersion. Under a mild condition, the class of distributions is shown to preserve both unimodality and moment existence. By adequately defining D, it is possible to generate skewed distributions. Using spline models on hyperspheres, we suggest a very general, yet practical, implementation for modelling directional dispersion in any dimension. Finally, we use the new class of distributions in a Bayesian regression setup and analyse the distributions of a set of biomedical measurements and a sample of U.S. manufacturing firms.

Suggested Citation

  • J.T.A.S. Ferreira & M.F.J. Steel, 2004. "Modelling Directional Dispersion Through Hyperspherical Log- Splines," Econometrics 0410006, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0410006
    Note: Type of Document - pdf; pages: 17
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/0410/0410006.pdf
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    References listed on IDEAS

    as
    1. Steel, M.F.J., 1991. "Bayesian Inference in Time Series," Papers 9153, Tilburg - Center for Economic Research.
    2. J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, EconWPA.
    3. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. José T.A.S. Ferreira & Miguel A Juárez & MArk F.J. Steel, 2005. "Directional Log-spline Distributions," Econometrics 0511001, EconWPA.
    2. Kamiya, Hidehiko & Takemura, Akimichi, 2008. "Hierarchical orbital decompositions and extended decomposable distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 339-357, March.

    More about this item

    Keywords

    Bayesian regression model; directional dispersion; elliptical distributions; existence of moments; modality; skewed distributions.;

    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

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