On the Tukey depth of an atomic measure |
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Authors: | A Hassairi O Regaieg |
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Institution: | aLaboratory of Probability and Statistics, Sfax University, BP 802, Sfax, Tunisia |
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Abstract: | This paper gives a relation between the convex Tukey trimmed region (see J.C. Massé, R. Theodorescu, Halfplane trimming for bivariate distributions, J. Multivariate Anal. 48(2) (1994) 188–202]) of an atomic measure and the support of the measure. It is shown that an atomic measure is concentrated on the extreme points of its Tukey trimmed region. A property concerning the extreme points which have 0 mass is given. As a corollary, we give a new method of proof of the Koshevoy characterization result. |
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Keywords: | Tukey depth Convex Support Tukey trimmed region |
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