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

Ivan Mizera and Milos Volauf

Journal of Multivariate Analysis, 2002, vol. 83, issue 2, 365-388

Abstract: 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 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.

Keywords: depth; depth; contours; maximum; depth; estimators; continuity; qualitative; robustness; stability; set-valued; analysis. (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (8)

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