Abstract
In a one-way analysis of variance, positive-part shrinkage versions of the R-estimators for the additive treatment constants are proposed, a long with amodified James-Stein estimation rule, when it is doubtful whether the parameters are null. The asymptotic distributional risks of the R-estimators, the proposed estimators, and the preliminary-test and shrinkage R-versions under an arbitrary quadratic loss are derived, and the relative risks arc studied. Under a special feasible quadratic loss, it is shown that the positive-part shrinkage R-estimators dominate the other estimators. R-estimators for the grand mean and for population means are discussed. The same discussions are presented for versions of the M-estimation.
