It is shown that the problem of asymptotic efficiency (in the Wolfowitz-sense) admits a satisfactory solution for the class of strongly asymptotically median unbiased estimators. The concept of strongly asymptotic median unbiasedness furthermore links up the classical approach (concerning estimator-sequences whose distribution functions converge) with Pfanzagl's concept of median unbiasedness.
"On the Asymptotic Efficiency of Strongly Asymptotically Median Unbiased Estimators." Ann. Statist. 6 (4) 920 - 922, July, 1978. https://doi.org/10.1214/aos/1176344266