The concept of $H_0$-contiguity is studied for certain nonparametric testing problems. Furthermore, it is shown that a meaningful sample definition of Pitman efficiency is possible under $H_0$-contiguity, and this definition turns out to coincide with the usual efficiency concept based on comparing asymptotic distributions.
Georg Neuhaus. "$H_0$-Contiguity in Nonparametric Testing Problems and Sample Pitman Efficiency." Ann. Statist. 10 (2) 575 - 582, June, 1982. https://doi.org/10.1214/aos/1176345798