We describe multivariate generalizations of the median, trimmed mean and $W$ estimates. The estimates are based on a geometric construction related to "projection pursuit." They are both affine equivariant (coordinate-free) and have high breakdown point. The generalization of the median has a breakdown point of at least $1/(d + 1)$ in dimension $d$ and the breakdown point can be as high as $1/3$ under symmetry. In contrast, various estimators based on rejecting apparent outliers and taking the mean of the remaining observations have breakdown points not larger than $1/(d + 1)$ in dimension $d$.
Publié le : 1992-12-14
Classification:
Multivariate depth and outlyingness,
location estimates,
robustness,
breakdown point,
projection pursuit,
halfspace distance,
Glivenko-Cantelli property,
62F35,
62G05,
62H12
@article{1176348890,
author = {Donoho, David L. and Gasko, Miriam},
title = {Breakdown Properties of Location Estimates Based on Halfspace Depth and Projected Outlyingness},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1803-1827},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348890}
}
Donoho, David L.; Gasko, Miriam. Breakdown Properties of Location Estimates Based on Halfspace Depth and Projected Outlyingness. Ann. Statist., Tome 20 (1992) no. 1, pp. 1803-1827. http://gdmltest.u-ga.fr/item/1176348890/