Impact of outliers on median-based and mean-based methods for anomalous diffusion exponent estimation

Abstract This study investigates the robustness of mean-based and median-based methods for estimating the anomalous diffusion (AnDi) exponent in particle trajectories. AnDi, observed in heterogeneous environments, presents challenges due to the presence of outliers that inevitably arise during the segmentation of trajectories into homogeneous sections. We focus on short trajectories modeled by two-dimensional fractional Brownian motion and explore alternative strategies for robust estimation. Specifically, we propose an adaptation of the time-averaged mean square displacement method that uses the median (or quantile) instead of the mean, as well as a mean-based approach that trims extreme squared displacements. Experiments conducted on synthetic datasets with controlled outlier characteristics, as well as on segmented trajectories from a benchmark dataset of the 2nd AnDi challenge, reveal that although median- and quantile-based methods effectively suppress high-variance outliers, they incur larger estimation errors compared to mean-based methods. In contrast, a mean-based method that trims a fixed percentage of the largest squared displacements achieves an improved balance between robustness and accuracy. Furthermore, our results suggest a critical strategy for segmenting heterogeneous trajectories: under conditions of uncertainty, ambiguous sections should be associated with segments exhibiting higher variance. This approach minimizes the influence of outliers on diffusion parameter estimation.