A nonparametric minimum Hellinger distance estimator of location is introduced and shown to be asymptotically efficient at every symmetric density with finite Fisher information. Under small, possibly asymmetric, perturbations in such a density, the estimator is asymptotically robust in a technical sense which extends Hajek's concept of "regularity." A numerical example illustrates the computational feasibility of the estimator and its resistance to an arbitrary single outlier.
@article{1176344125,
author = {Beran, Rudolf},
title = {An Efficient and Robust Adaptive Estimator of Location},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 292-313},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344125}
}
Beran, Rudolf. An Efficient and Robust Adaptive Estimator of Location. Ann. Statist., Tome 6 (1978) no. 1, pp. 292-313. http://gdmltest.u-ga.fr/item/1176344125/