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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) α-interquantile ranges and (ii) mixtures of at most two α-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.