A robust estimator for the mean direction of the von Mises-Fisher distribution

The von Mises-Fisher distribution is probably the most widely used distribution to model data on the (hyper)sphere. Characterized by two parameters, the mean direction and concentration parameter, it is symmetrical about the mean direction. The Maximum Likelihood estimator for this parameter is the directional sample mean. However, this estimator is not robust. Although the estimation result cannot be corrupted arbitrarily (but only up to a certain amount) the need for some alternative (robust) estimators has been recognized. Within this work, it is first discussed how the robustness of a directional location estimator can be evaluated. Then, a new robust estimator of the mean direction is introduced.