The superiority of the Bayes linear unbiased minimum Variance estimator under balanced loss function

The superiority of the Bayes linear unbiased minimum variance(BLUMV) estimator with respect to the optimally weighted least square(OWLS) estimator of unknown parameter was studied in terms of the balanced loss risk function criterion,and the two estimators can converge to the same one under a certain condition.The superiority of the BLUMV estimator over the OWLS estimator was studied under predictive Pitman closeness(PRPC) criterion.