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.
Publié le : 1997-10-14
Classification:
Trimmed regions,
data depth,
expectile,
multivariate median,
quantile,
62H05,
52A22,
60F05
@article{1069362382,
author = {Koshevoy, Gleb and Mosler, Karl},
title = {Zonoid trimming for multivariate distributions},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 1998-2017},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362382}
}
Koshevoy, Gleb; Mosler, Karl. Zonoid trimming for multivariate distributions. Ann. Statist., Tome 25 (1997) no. 6, pp. 1998-2017. http://gdmltest.u-ga.fr/item/1069362382/