Some standard robustness concepts, developed for linear data, are found wanting in the case of directional data. We introduce a standardized bias robustness allowing for uniform robustness considerations of statistics for bounded parameter spaces. Specifically, we verify the nonrobustness in this sense of the directional mean, the directional dispersion and the maximum likelihood estimator of the concentration parameter of the von Mises-Fisher distributions.
"Robustness of Estimators for Directional Data." Ann. Statist. 16 (2) 609 - 618, June, 1988. https://doi.org/10.1214/aos/1176350822