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October 1997 Zonoid trimming for multivariate distributions
Gleb Koshevoy, Karl Mosler
Ann. Statist. 25(5): 1998-2017 (October 1997). DOI: 10.1214/aos/1069362382

Abstract

A family of trimmed regions is introduced for a probability distribution in Euclidean d-space. The regions decrease with their parameter $\alpha$, from the closed convex hull of support (at $\alpha = 0$) to the expectation vector (at $\alpha = 1$). The family determines the underlying distribution uniquely. For every $\alpha$ the region is affine equivariant and continuous with respect to weak convergence of distributions. The behavior under mixture and dilation is studied. A new concept of data depth is introduced and investigated. Finally, a trimming transform is constructed that injectively maps a given distribution to a distribution having a unique median.

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Gleb Koshevoy. Karl Mosler. "Zonoid trimming for multivariate distributions." Ann. Statist. 25 (5) 1998 - 2017, October 1997. https://doi.org/10.1214/aos/1069362382

Information

Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0881.62059
MathSciNet: MR1474078
Digital Object Identifier: 10.1214/aos/1069362382

Subjects:
Primary: 62H05
Secondary: 52A22, 60F05

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 1997
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