We derive the asymptotic distribution ofthe maximal depth
regression estimator recently proposed in Rousseeuw and Hubert. The estimator
is obtained by maximizing a projection-based depth and the limiting
distribution is characterized through a max–min operation of a
continuous process. The same techniques can be used to obtain the limiting
distribution of some other depth estimators including Tukey’s deepest
point based on half-space depth. Results for the special case of
two-dimensional problems have been available, but the earlier arguments have
relied on some special geometric properties in the low-dimensional space. This
paper completes the extension to higher dimensions for both regression and
multivariate location models.
@article{1017939144,
author = {Bai, Zhi-Dong and He, Xuming},
title = {Asymptotic distributions of the maximal depth estimators for
regression and multivariate location},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1616-1637},
language = {en},
url = {http://dml.mathdoc.fr/item/1017939144}
}
Bai, Zhi-Dong; He, Xuming. Asymptotic distributions of the maximal depth estimators for
regression and multivariate location. Ann. Statist., Tome 27 (1999) no. 4, pp. 1616-1637. http://gdmltest.u-ga.fr/item/1017939144/