Asymptotic expansions are established for the power of distribution-free tests in the two-sample problem. These expansions are then used to obtain deficiencies in the sense of Hodges and Lehmann for distribution-free tests with respect to their parametric competitors and for the estimators of shift associated with these tests.
"Asymptotic Expansions for the Power of Distributionfree Tests in the Two-Sample Problem." Ann. Statist. 6 (5) 937 - 1004, September, 1978. https://doi.org/10.1214/aos/1176344305