An Efficient and Robust Adaptive Estimator of Location

Abstract

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.