Penalized Maximum Likelihood Estimator for Mixture of von Mises-Fisher Distributions

Tin Lok James Ng

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arXiv · 2009.02921

Penalized Maximum Likelihood Estimator for Mixture of von Mises-Fisher Distributions

Tin Lok James Ng

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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 simulation studies are performed to examine its performance.

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BibTeX RIS

Tin Lok James Ng. 2022-03-05. Penalized Maximum Likelihood Estimator for Mixture of von Mises-Fisher Distributions. https://arxiv.org/abs/2009.02921

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