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…
24 Citations
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This thesis discusses three depth functions: two well-known depth functions halfspace depth and simplicial depth, and one recently defined depth function named as β-skeleton depth, β ≥ 1, which is equivalent to the previously defined spherical depth and lens depth.
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