Nonparametric analysis of directional data based on data depth

Data depth is a statistical method whose primary aim is to order data of a reference space according to centrality. This is particularly appealing for directional data because no standard ordering is available, not even in the circular case. Moreover, the depth approach deals in a natural way with the peculiar aspects of directional data, i.e., the lack of a zero-direction and the wrap-around effect. The paper reviews the data depth program concentrating on typical applications to directional distributions and data. Two geometrical depth functions, simplicial depth and Tukey’s depth, are considered. Several depth-based summaries, including angular medians, depth regions and dispersion parameters are illustrated, the latter with some novel results. Examples cover symmetric and asymmetric distributions as well as real-data applications.