Local depth-based classification of directional data

Abstract

Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward ordering of the data. This work aims at proposing the use of a local notion of data depth function to be applied in the DD-plot (Depth vs. Depth plot) to classify directional data. The proposed method is investigated through an extensive simulation study and two real-data examples.