Modelling directional dispersion through hyperspherical log-splines
AbstractWe 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. Copyright 2005 Royal Statistical Society.
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Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society Series B.
Volume (Year): 67 (2005)
Issue (Month): 4 ()
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Other versions of this item:
- J.T.A.S. Ferreira & M.F.J. Steel, 2004. "Modelling Directional Dispersion Through Hyperspherical Log- Splines," Econometrics 0410006, EconWPA.
- 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
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.:
- Osiewalski, Jacek & Steel, Mark F.J., . "Robust Bayesian inference in Iq-Spherical models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/2843, Universidad Carlos III de Madrid.
- Steel, M.F.J., 1991.
"Bayesian Inference in Time Series,"
9153, Tilburg - Center for Economic Research.
- J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, EconWPA.
- Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
- José T.A.S. Ferreira & Miguel A Juárez & MArk F.J. Steel, 2005. "Directional Log-spline Distributions," Econometrics 0511001, EconWPA.
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