Continuity of Halfspace Depth Contours and Maximum Depth Estimators: Diagnostics of Depth-Related Methods

@article{Mizera2002ContinuityOH,
  title={Continuity of Halfspace Depth Contours and Maximum Depth Estimators: Diagnostics of Depth-Related Methods},
  author={Ivan Mizera and Milos Volauf},
  journal={Journal of Multivariate Analysis},
  year={2002},
  volume={83},
  pages={365-388}
}
Continuity of procedures based on the halfspace (Tukey) depth (location and regression setting) is investigated in the framework of continuity concepts from set-valued analysis. Investigated procedures are depth contours (upper level sets) and maximum depth estimators. Continuity is studied both as the pointwise continuity of data-analytic functions, and the weak continuity of statistical functionals--the latter having relevance for qualitative robustness. After a real-data example, some… 
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