Contours of depth often provide a good geometrical understanding of the structure of a multivariate dataset. They are also useful in robust statistics in connection with generalized medians and data ordering. If the data constitute a random sample from a spherical or elliptic distribution, the depth contours are generally required to converge to spherical or elliptical shapes. We consider contour constructions based on a notion of data depth and
prove a uniform contour convergence theorem under verifiable conditions on the depth measure. Applications to several existing depth measures discussed in the literature are also considered.
Publié le : 1997-04-14
Classification:
Convergence,
contour,
data depth,
elliptic distributions,
location-scatter,
$M$-estimator,
multivariate dataset,
robustness,
62H12,
62F35,
62H05,
60H05
@article{1031833661,
author = {He, Xuming and Wang, Gang},
title = {Convergence of depth contours for multivariate datasets},
journal = {Ann. Statist.},
volume = {25},
number = {6},
year = {1997},
pages = { 495-504},
language = {en},
url = {http://dml.mathdoc.fr/item/1031833661}
}
He, Xuming; Wang, Gang. Convergence of depth contours for multivariate datasets. Ann. Statist., Tome 25 (1997) no. 6, pp. 495-504. http://gdmltest.u-ga.fr/item/1031833661/