Directional DD-classifiers under non-rotational symmetry

A directional random variable is rotationally symmetric around a location parameter if its distribution only depends on the angle between the value the variable can take and the location parameter itself. This is clearly an oversimplified model. On the other hand, the performance of depth-based classifiers for directional data has been widely studied only under the case of rotational symmetry of the underlying class distributions. For this reason, this work aims at evaluating the efficacy of some of them under non-rotational symmetry. Particularly, the DD-classifiers exploiting the linear, quadratic, and KNN discriminant rules when associated with angular distance-based depths are examined. Their performances under Kent distributions are investigated by means of a simulation study. As a benchmark, the directional Bayes rule is considered. In passing, these classifiers are also reviewed, noting that the way they work within the directional data domain has been given a bit for granted within the literature.