In the multivariate one sample location problem, the theory of permutation distribution under sign-invariant transformations is extended to a class of rank order statistics, and this is utilized in the formulation of a genuinely distribution free class of rank order tests for location (based on Chernoff-Savage (1958) type of test-statistics). Asymptotic properties of these permutationally distribution free rank order tests are studied, and certain stochastic equivalence relations with a similar class of multivariate extensions of one sample Chernoff-Savage type of tests are derived. The power properties of these tests are studied.
"On the Theory of Rank Order Tests for Location in the Multivariate One Sample Problem." Ann. Math. Statist. 38 (4) 1216 - 1228, August, 1967. https://doi.org/10.1214/aoms/1177698790