Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that $S$-estimators satisfy an exact Holder condition of order 1/2 at models with normal errors. In Section 5 the breakdown points of the Hampel-Krasker dispersion and regression functionals are shown to be 0. The exact breakdown point of the Krasker-Welsch dispersion functional is obtained as well as bounds for the corresponding regression functional. Section 6 contains the construction of a linearly equivariant, high breakdown and locally Lipschitz dispersion functional for any design distribution. In Section 7 it is shown that there is no inherent contradiction between efficiency and a high breakdown point. Section 8 contains a linearly equivariant, high breakdown regression functional which is Lipschitz continuous at models with normal errors.
Publié le : 1993-12-14
Classification:
Influence function,
Lipschitz continuity,
global definability,
breakdown point,
linear equivariance,
62F35,
62J05
@article{1176349401,
author = {Davies, P. L.},
title = {Aspects of Robust Linear Regression},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 1843-1899},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349401}
}
Davies, P. L. Aspects of Robust Linear Regression. Ann. Statist., Tome 21 (1993) no. 1, pp. 1843-1899. http://gdmltest.u-ga.fr/item/1176349401/