Continuity of Halfspace Depth Contours and Maximum Depth Estimators: Diagnostics of Depth-Related Methods
✍ Scribed by Ivan Mizera; Milos Volauf
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 206 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0047-259X
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✦ Synopsis
Continuity of procedures based on the halfspace (Tukey) depth (location and regression setting) is investigated in the framework of continuity concepts from setvalued 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 general criteria and counterexamples are given, as well as positive results holding for ''typical'' data. Finally, some consequences for diagnostics and practical use of the depth-based techniques are drawn.