A spatial rank test and corresponding estimators for several samples

In the several samples location problem, it is usually of interest to present estimates of treatment effects along with the test. The spatial Hodges-Lehmann estimators Δ^ij of the differences between treatments i and j are apparent companions to a multivariate Kruskal-Wallis test. However, these estimators generally fail to satisfy the property Δ^ij=Δ^ik+Δ^kj, making them incompatible with each other. In this paper we consider adjusted estimators possessing this property. A simulation study is carried out in order to study their finite sample efficiencies. Limiting distributions and efficiencies are presented as well.