S. Liebscher et al. Robust parameter estimation for von Mises-Fisher distribution A robust estimator for the mean direction of the von Mises-Fisher distribution S. Liebscher 1∗ , T. Kirschstein 1 , G. Pandolfo 2 , G.C. Porzio 2 and G. Ragozini 3 1 Martin-Luther-University Halle-Wittenberg, Große Steinstraße 73, D-06099 Halle (Saale), Germany; steffen.liebscher@wiwi.uni-halle.de, thomas.kirschstein@wiwi.uni-halle.de. 2 University of Cassino and Southern Lazio, Via San Angelo, localita Folcara, I-03043 Cassino, Italy; giuseppepandolfo1@virgilio.it, porzio@unicas.it. 3 University of Naples Federico II, Via L. Rodin` o 22, I-80138, Napoli, Italy; gian- carlo.ragozini@unina.it. ∗ Presenting author Keywords. Directional data; Robust estimation; Von Mises-Fisher distribution. The von Mises-Fisher (or Langevin) distribution is commonly used to describe the distribution of data on the (hyper)sphere. The distribution has two parameters: the mean direction μ and the concentration parameter κ (with 0 ≤ κ ≤∞), is unimodal (for κ> 0), and symmetrical about μ. Estimators for both parameters are readily available for some time (???). While robustness issues have been taken into consideration when estimating the concentration parameter (???), robustness has only recently been discussed when estimating the mean direction (?). This is mainly due to a common and persistent misconception that non-robustness does not constitute a serious problem when working with directional data (especially when talking about the mean direction, as the directional difference between any two points on the (hyper)sphere can only be 180 ◦ or π at the maximum). In this paper the measurement of robustness of mean direction estimators is recon- sidered. A new measure to assess the robustness based on the maximum bias is introduced. This measure provides the foundation to derive a definition of break- down of an estimator similar in concept to the well-known finite sample breakdown point. Finally, a new estimator for the mean direction of the von Mises-Fisher dis- tribution is proposed which is shown to deliver consistent estimates as well as being robust in terms of the newly introduced measures of robustness. Results of a simu- lation study indicate that the new estimator is more robust than the approach by ? and much more robust than the standard ML estimator for certain contamination schemes. International Conference on Robust Statistics 2016 1