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Penalized maximum likelihood estimator for mixture of von Mises–Fisher distributions

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  • Tin Lok James Ng

    (Trinity College Dublin)

Abstract

The von Mises–Fisher distribution is one of the most widely used probability distributions to describe directional data. Finite mixtures of von Mises–Fisher distributions have found numerous applications. However, the likelihood function for the finite mixture of von Mises–Fisher distributions is unbounded and consequently the maximum likelihood estimation is not well defined. To address the problem of likelihood degeneracy, we consider a penalized maximum likelihood approach whereby a penalty function is incorporated. We prove strong consistency of the resulting estimator. An Expectation–Maximization algorithm for the penalized likelihood function is developed and experiments are performed to examine its performance.

Suggested Citation

  • Tin Lok James Ng, 2023. "Penalized maximum likelihood estimator for mixture of von Mises–Fisher distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 181-203, February.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:2:d:10.1007_s00184-022-00867-0
    DOI: 10.1007/s00184-022-00867-0
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    References listed on IDEAS

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    1. Gabriela Ciuperca & Andrea Ridolfi & Jérôme Idier, 2003. "Penalized Maximum Likelihood Estimator for Normal Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 45-59, March.
    2. Hornik, Kurt & Grün, Bettina, 2014. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i10).
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