In this paper we consider a partial ordering that is "between" the stochastic ordering defined by Lehmann (1955) and an ordering associated with the monotone likelihood ratio property. A tail ordering deduced from it is applied to the comparison of the asymptotic efficiencies of rank tests in the two-sample problem. In particular, we show that the asymptotic relative efficiency of two rank tests preserve this tail ordering if one score function is "more convex" than the other.
"Tail Ordering and Asymptotic Efficiency of Rank Tests." Ann. Statist. 16 (1) 470 - 478, March, 1988. https://doi.org/10.1214/aos/1176350715