Estimation of normal means in the tree order model by the weighting methods

Abstract

Consider k + 1 independent normal populations with the tree order restriction on the mean parameters. For the tree order model, the restricted estimator of control group parameter is dominated by the unrestricted estimator when the number of treatment groups is large. We discuss two techniques for reducing of mean squared error via to the two weighting methods which are dissimilarity and conditional Bayesian criteria. Based on the bias and mean squared error criteria, the performance of the proposed estimators is compared with the alternative estimators in order to search for a better estimator. Although the superior estimator that uniformly dominates the others does not exist in general, but the proposed estimators dominate the corresponding unrestricted estimator and compete very well with the other alternative estimators introduced by the authors.