The depth of multivariate data can be used to construct weighted means as robust estimators of location. The use of projection depth leads to the Stahel-Donoho estimator as a special case. In contrast to maximal depth estimators, the depth-weighted means are shown to be asymptotically normal under appropriate conditions met by depth functions commonly used in the current literature. We also confirm through a finite-sample study that the Stahel-Donoho estimator achieves a desirable balance between robustness and efficiency at Gaussian models.
Publié le : 2004-02-14
Classification:
Asymptotic normality,
depth,
breakdown point,
efficiency,
projection depth,
$L$-estimator,
robustness,
62E20,
62F12,
62G35,
62F35
@article{1079120132,
author = {Zuo, Yijun and Cui, Hengjian and He, Xuming},
title = {On the Stahel-Donoho estimator and depth-weighted means of multivariate data},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 167-188},
language = {en},
url = {http://dml.mathdoc.fr/item/1079120132}
}
Zuo, Yijun; Cui, Hengjian; He, Xuming. On the Stahel-Donoho estimator and depth-weighted means of multivariate data. Ann. Statist., Tome 32 (2004) no. 1, pp. 167-188. http://gdmltest.u-ga.fr/item/1079120132/