The interpoint depth for directional data

The notion of interpoint depth is applied to spherical spaces by using an appropriate angular distance function for data lying on the surface of the unit hypersphere. The traditional multivariate methods, indeed, are not suitable for the analysis of directional data and this holds true also for distance measures and related depth-based methods. The interpoint depth for directional data possesses some nice properties and can be used for high dimensional data analysis. This notion of depth is particularly useful to investigate local features of distribution, such as multimodality, and can be exploited to deal with many statistical problems. The behavior of the proposed depth is investigated by means of simulated data. In addition, three interesting applications are presented.