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Description
Directional data consist of observations that lie on a unit sphere. Although the sample space is compact, outliers can still occur in practice, particularly when the data are highly concentrated. This motivates the development of robust estimation methods for directional models. Robust inference for directional data has therefore become a popular topic in recent statistical research. In this study, we propose a minimum Hellinger distance estimator (MHDE) for directional data on a sphere. While MHDE estimators are well understood in Euclidean settings, where they achieve robustness and first-order efficiency, their theoretical properties on the sphere remain largely unexplored. We establish the asymptotic normality of the proposed estimator under suitable regularity conditions. Our results show that the MHDE retains efficiency when the model is correctly specified while providing robustness against model deviations. This confirms that, as in the Euclidean setting, the estimator achieves robustness without sacrificing efficiency. Additionally, we conduct numerical experiments to investigate the finite-sample performance of the proposed method. The results corroborate the theoretical findings and demonstrate the estimator's practical effectiveness.