  Robust estimation of location and concentration parameters for the von
Mises-Fisher distribution is discussed. A key reparametrisation is achieved by
expressing the two parameters as one vector on the Euclidean space. With this
representation, we first show that maximum likelihood estimator for the von
Mises-Fisher distribution is not robust in some situations. Then we propose two
families of robust estimators which can be derived as minimisers of two density
power divergences. The presented families enable us to estimate both location
and concentration parameters simultaneously. Some properties of the estimators
are explored. Simple iterative algorithms are suggested to find the estimates
numerically. A comparison with the existing robust estimators is given as well
as discussion on difference and similarity between the two proposed estimators.
A simulation study is made to evaluate finite sample performance of the
estimators. We consider a sea star dataset and discuss the selection of the
tuning parameters and outlier detection.
