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Modelling directional dispersion through hyperspherical log‐splines

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  • José T. A. S. Ferreira
  • Mark F. J. Steel

Abstract

Summary. We introduce the directionally dispersed class of multivariate distributions, a generalization 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 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 flexible, yet practical, implementation for modelling directional dispersion in any dimension. Finally, we use the new class of distributions in a Bayesian regression set‐up and analyse the distributions of a set of biomedical measurements and a sample of US manufacturing firms.

Suggested Citation

  • 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, September.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:4:p:599-616
    DOI: 10.1111/j.1467-9868.2005.00518.x
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    References listed on IDEAS

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    1. Osiewalski, Jacek & Steel, Mark F.J., 1992. "Robust Bayesian inference in Iq-Spherical models," UC3M Working papers. Economics 2843, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Steel, M.F.J., 1991. "Bayesian inference in time series," Discussion Paper 1991-53, Tilburg University, Center for Economic Research.
    3. J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, University Library of Munich, Germany.
    4. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, University Library of Munich, Germany.
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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, University Library of Munich, Germany.
    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.

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    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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