Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution

@article{Hasannasab2021AlternativesTT,
  title={Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution},
  author={Marzieh Hasannasab and Johannes Hertrich and Friederike Laus and Gabriele Steidl},
  journal={Numer. Algorithms},
  year={2021},
  volume={87},
  pages={77-118}
}
In this paper, we consider maximum likelihood estimations of the degree of freedom parameter ν, the location parameter μ and the scatter matrix Σ of the multivariate Student t distribution. In particular, we are interested in estimating the degree of freedom parameter ν that determines the tails of the corresponding probability density function and was rarely considered in detail in the literature so far. We prove that under certain assumptions a minimizer of the negative log-likelihood… 
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