Abstract

Environmental variables such as wind direction, ocean currents, and animal movement trajectories are inherently circular and often exhibit irregular behavior, including outliers and departures from standard distributional assumptions. The periodic nature of these observations introduces specific challenges, requiring estimation methods that appropriately account for the circular structure of the data. Classical circular estimation procedures can be sensitive to anomalous observations, potentially affecting the reliability and stability of the resulting estimates. These challenges highlight the importance of developing robust statistical approaches specifically suited to circular data.
In this work, we propose an M-estimation framework based on a loss function specifically designed for circular data, accounting for the periodic nature of angular observations. The proposed approach aims to reduce the influence of atypical observations while preserving desirable statistical properties. Within this framework, we introduce a robust S-scale estimator adapted to the circular setting and investigate its robustness properties. The performance of the proposed estimator is evaluated through simulations under different contamination scenarios and compared with existing robust estimation methods. Finally, we illustrate the use of the proposed estimator through the analysis of environmental directional data.