Minimax asymptotic mean-squared-error of L-estimators of scale parameter

We derive the AMSE (maximal asymptotic mean-squared-error) of the general class of L-estimators of scale that are location-scale equivariant and Fisher consistent. For non-normal error distributions, we determined estimators that have minimum AMSE over the subclass of (i) -interquantile ranges and (ii) mixtures of at most two -interquantile ranges. Finally, the L-estimators of scale symmetrized about the median were found to have the same AMSE as their nonsymmetrized counterparts, thus yielding the same results as in the symmetrized case.