Distance‐based depths for directional data

@article{Pandolfo2018DistancebasedDF,
  title={Distance‐based depths for directional data},
  author={Giuseppe Pandolfo and Davy Paindaveine and Giovanni Camillo Porzio},
  journal={Canadian Journal of Statistics},
  year={2018},
  volume={46}
}
Directional data are constrained to lie on the unit sphere of ℝq for some q ≥ 2. To address the lack of a natural ordering for such data, depth functions have been defined on spheres. However, the depths available either lack flexibility or are so computationally expensive that they can only be used for very small dimensions q. In this work, we improve on this by introducing a class of distance‐based depths for directional data. Irrespective of the distance adopted, these depths can easily be… 
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