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.
"An Efficient and Robust Adaptive Estimator of Location." Ann. Statist. 6 (2) 292 - 313, March, 1978. https://doi.org/10.1214/aos/1176344125