Improved biased estimation in an ANOVA model

AbstractThe problem of simultaneous estimation of means in one-way analysis of variance (ANOVA) is considered when it is suspected that the mean parameters are equal, but with some degree of uncertainty. Improved estimators using Stein-rule and preliminary test approach are proposed. The explicit forms of the biases and risk functions of the proposed estimators are derived. The relative performance of the positive-part Stein-rule estimator (PSE) and the usual Stein-rule estimator (SE) is critically assessed with the aid of the quadratic loss function. It is shown analytically as well as computationally that PSE dominates the classical SE in the whole parameter space. Also the improved preliminary test estimator (IPE) is shown to have smaller risk than that of the classical PE in the entire parameter space