It is shown under appropriate conditions that Rousseeuw's minimum volume estimator and other $S$-estimators of multivariate location and dispersion parameters are consistent. Under certain differentiability conditions the estimates are asymptotically normally distributed with a norming factor of $n^{1/2}$.
Publié le : 1987-09-14
Classification:
$S$-estimators,
multivariate location and dispersion parameters,
consistency,
asymptotic normality,
finite sample breakdown points,
random search,
62F10,
62E20,
62H99
@article{1176350505,
author = {Davies, P. L.},
title = {Asymptotic Behaviour of $S$-Estimates of Multivariate Location Parameters and Dispersion Matrices},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 1269-1292},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350505}
}
Davies, P. L. Asymptotic Behaviour of $S$-Estimates of Multivariate Location Parameters and Dispersion Matrices. Ann. Statist., Tome 15 (1987) no. 1, pp. 1269-1292. http://gdmltest.u-ga.fr/item/1176350505/