Multiple Comparisons Based on R-estimators in the One-Way Layout

Abstract

In a one-way analysis of variance model, robust versions based on R-estimators are proposed for single-step multiple comparisons procedures discussed by Tukey (1953), Dunnett (1955), and Scheffé (1953). The robust procedures are two methods based on joint ranks and pairwise ranks. It is shown that the two methods are asymptotically equivalent. Although we fail to construct simultaneous tests based on linear joint ranks, we are able to propose simultaneous tests based on the R-estimators. Robustness for asymptotic properties is discussed. The accuracy of asymptotic approximation is investigated.