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

Tin Lok James Ng ()
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Tin Lok James Ng: Trinity College Dublin

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 2, No 2, 203 pages

Abstract: 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.

Keywords: Mixture of von Mises–Fisher distributions; Penalized maximum likelihood estimation; Strong consistency (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00184-022-00867-0

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