An asymptotically efficient sequence of estimators for the location parameter of an (unknown) symmetric density $f$ is given under weak conditions on the tails of $f$. The estimators are related to the usual linear combination of order statistics except that the unknown $f$ has to be estimated and only some of the order statistics are used.
"An Asymptotically Efficient Sequence of Estimators of a Location Parameter." Ann. Statist. 3 (2) 285 - 298, March, 1975. https://doi.org/10.1214/aos/1176343057