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A semi-parametric model for circular data based on mixtures of beta distributions

  • Jose Antonio Carnicero


  • Michael P. Wiper


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    This paper introduces a new, semi-parametric model for circular data, based on mixtures of shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial density model which is well known to provide good approximations to any density with finite support and it is shown that, as for the Bernstein polynomial model, the trigonometric moments of the SSB mixture model can all be derived. Two methods of fitting the SSB mixture model are considered. Firstly, a classical, maximum likelihood approach for fitting mixtures of a given number of SSB components is introduced. The Bayesian information criterion is then used for model selection. Secondly, a Bayesian approach using Gibbs sampling is considered. In this case, the number of mixture components is selected via an appropriate deviance information criterion. Both approaches are illustrated with real data sets and the results are compared with those obtained using Bernstein polynomials and mixtures of von Mises distributions.

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    Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws081305.

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    Date of creation: Mar 2008
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    Handle: RePEc:cte:wsrepe:ws081305
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    1. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100.
    2. José T.A.S. Ferreira & Miguel A Juárez & MArk F.J. Steel, 2005. "Directional Log-spline Distributions," Econometrics 0511001, EconWPA.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    4. J. J. Fernández-Durán, 2004. "Circular Distributions Based on Nonnegative Trigonometric Sums," Biometrics, The International Biometric Society, vol. 60(2), pages 499-503, 06.
    5. A. Mooney, Jennifer & Helms, Peter J. & Jolliffe, Ian T., 2003. "Fitting mixtures of von Mises distributions: a case study involving sudden infant death syndrome," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 505-513, January.
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