We investigate the asymptotic behavior of a weighted sample mean
and covariance,where the weights are determined by the Mahalanobis distances
with respect to initial robust estimators.We derive an explicit expansion for
the weighted estimators. From this expansion it can be seen that reweighting
does not improve the rate of convergence of the initial estimators.We also show
that if one uses smooth $S$-estimators to determine the weights, the weighted
estimators are asymptotically normal. Finally, we will compare the efficiency
and local robustness of the reweighted $S$-estimators with two other
improvements of $S$-estimators: $\tau$-estimators and constrained
$M$-estimators.
Publié le : 1999-10-14
Classification:
Robust estimation of multivariate location and
covariance,
reweighted least squares,
application of empirical process theory,
62E20,
62F12,
62F35,
62H10,
62H12
@article{1017939145,
author = {Lopuha\"a, Hendrik P.},
title = {Asymptotics of reweighted estimators of multivariate location
and scatter},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1638-1665},
language = {en},
url = {http://dml.mathdoc.fr/item/1017939145}
}
Lopuhaä, Hendrik P. Asymptotics of reweighted estimators of multivariate location
and scatter. Ann. Statist., Tome 27 (1999) no. 4, pp. 1638-1665. http://gdmltest.u-ga.fr/item/1017939145/