Asymptotic expansions are established for the power of distribution free tests in the one-sample problem. These expansions are then used to obtain deficiencies in the sense of Hodges and Lehmann (1970) for distribution free tests with respect to their parametric competitors and for the estimators of location associated with these tests.
"Asymptotic Expansions for the Power of Distribution Free Tests in the One-Sample Problem." Ann. Statist. 4 (1) 108 - 156, January, 1976. https://doi.org/10.1214/aos/1176343350