Halfspace depths for scatter, concentration and shape matrices

@article{Paindaveine2018HalfspaceDF,
  title={Halfspace depths for scatter, concentration and shape matrices},
  author={Davy Paindaveine and Germain Van Bever},
  journal={The Annals of Statistics},
  year={2018}
}
We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept extends the one from Chen, Gao and Ren (2015) to the non-centered case, and is in the same spirit as the one in Zhang (2002). Rather than focusing, as in these earlier works, on deepest scatter matrices, we thoroughly investigate the properties of the proposed depth and of the corresponding depth regions. We do so under minimal assumptions and, in particular, we do not restrict… 

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