Non-Parametric Estimation of Location

A sequence of asymptotically normally distributed estimators of location is presented, having the property that, for any epsilon 0, all estimators in the sequence beyond an appropriate point have asymptotic variances within epsilon of the Cramer-Rao lower bound, uniformly for all symmetric distributions in a non-parametric family constrained only by regularity conditions. The simplest non-trivial estimator in this sequence already possesses good efficiency-robustness properties, both asymptotically and for small sample sizes. This estimator is much easier to compute than previously proposed estimators having similar properties, and a good non-parametric estimate of the variance of the location estimator is produced as a byproduct.