Halfspace depth and floating body
| Autor: | Carsten Schütt, Elisabeth M. Werner, Stanislav Nagy |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Surface (mathematics) halfspace depth Generalization measures of symmetry 01 natural sciences Measure (mathematics) statistical depth Affine geometry 010104 statistics & probability 0502 economics and business Euclidean geometry 62H05 0101 mathematics 050205 econometrics Mathematics 05 social sciences Mathematical analysis Regular polygon 52A20 Floating body Tukey depth Affine transformation 62G35 Statistics Probability and Uncertainty Symmetry (geometry) 62H11 62H99 |
| Zdroj: | Statist. Surv. 13 (2019), 52-118 |
| Popis: | Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Maximum halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the maximum depth stands as a generalization of a measure of symmetry for convex sets, well studied in geometry. Under a mild assumption, the upper level sets of the halfspace depth coincide with the convex floating bodies of measures used in the definition of the affine surface area for convex bodies in Euclidean spaces. These connections enable us to partially resolve some persistent open problems regarding theoretical properties of the depth. |
| Databáze: | OpenAIRE |
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