For multivariate data, the halfspace depth function can be seen as a natural and affine equivariant generalization of the univariate empirical cdf. For any multivariate data set, we show that the resulting halfspace depth function completely determines the empirical distribution. We do this by actua
A Characterization of Halfspace Depth
โ Scribed by Emilio Carrizosa
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 249 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0047-259X
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โฆ Synopsis
In this note we present a characterization of halfspace depth which relates it with well-known concepts of Locational Analysis. This characterization also leads to a natural extension of the concept of depth to noneuclidean location estimation as well as other settings like regression.
๐ SIMILAR VOLUMES
The sensitivity of halfspace depth values and contours to perturbations of the underlying distribution is investigated. The influence function of the halfspace depth of any point x # R p is bounded and discontinuous; it is constant and positive when the perturbing observation z is placed in any opti
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 t
We characterize finite index depth 2 inclusions of type II 1 factors in terms of actions of weak Kac algebras and weak C\*-Hopf algebras. If N/M/M 1 / M 2 / } } } is the Jones tower constructed from such an inclusion N/M, then B= M$ & M 2 has a natural structure of a weak C\*-Hopf algebra and there