R-Estimators and confidence regions for treatment effects in multi-response experiments

A class of rank estimators of treatment effects in a two-way MANOVA model without interaction is considered. Asymptotic distributions of the R-estimators as the number of blocks tends to infinity are derived. Based on the R-estimators and their asymptotic distributions, confidence regions for the treatment effects are proposed. The asymptotic relative efficiencies of the nonparametric procedures relative to the classical procedures based on unbiased estimators are investigated.