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Approximate likelihood inference for the Bingham distribution

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  • Marco Bee
  • Roberto Benedetti
  • Giuseppe Espa

Abstract

Likelihood inference for the Bingham distribution is difficult because the density function contains a normalization constant that cannot be computed in closed form. We propose to estimate the parameters by means of Approximate Maximum Likelihood Estimation (AMLE), thus bypassing the problem of evaluating the likelihood function. We study the impact of the input parameters of the AMLE algorithm and suggest some methods for choosing their numerical values. Moreover, we compare AMLE to the standard approach consisting in maximizing numerically the (approximate) likelihood obtained with the normalization constant estimated via the Holonomic Gradient Method (HGM). For the Bingham distribution on the sphere, simulation experiments and real-data applications produce similar outcomes for both methods. On the other hand, AMLE outperforms HGM when the dimension increases.

Suggested Citation

  • Marco Bee & Roberto Benedetti & Giuseppe Espa, 2015. "Approximate likelihood inference for the Bingham distribution," DEM Working Papers 2015/02, Department of Economics and Management.
    • Handle: RePEc:trn:utwprg:2015/02
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    References listed on IDEAS

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    1. Kume, A. & Walker, S.G., 2014. "On the Bingham distribution with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 345-352.
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    4. A. Kume & Andrew T. A. Wood, 2005. "Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants," Biometrika, Biometrika Trust, vol. 92(2), pages 465-476, June.
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    Keywords

    Directional data; Simulation; Intractable Likelihood; Sufficient statistics;
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