IMPROVED ESTIMATION FOR THE COMPONENT MEAN-VECTOR

抄録

This article discusses four estimation methods for the first component mean vector μ₁ of a q-variate normal distribution when it is suspected that μ₁=μ₂, where μ₂ is the second component mean vector. Exact bias and risks of all of these estimators are derived and their efficiencies relative to a classical estimators are studied. An optimum rule for the preliminary test estimator (PTE) is discussed. The range in the parameter space where preliminary test estimator dominates shrinkage estimator is investigated. It is shown that the Stein-rule estimator (SE) dominates the classical one, whereas none of the PTE and SE dominate each other. The range in the parameter space where PTE dominates SE is also investigated. It is found that SE outperforms the PTE except in a range around the null hypothesis. Further, for large values of α, the level of statistical significance, SE dominates the PTE uniformly. The relative dominance picture of the estimators is presented.