The bias of the unbiased estimator: a study of the iterative application of the BLUE method

摘要

The best linear unbiased estimator (BLUE) is a popular statistical methodadopted to combine multiple measurements of the same observable taking intoaccount individual uncertainties and their correlation. The method is unbiasedby construction if the true uncertainties and their correlation are known, butit may exhibit a bias if uncertainty estimates are used in place of the trueones, in particular if those estimated uncertainties depend on measured values.This is the case for instance when contributions to the total uncertainty areknown as relative uncertainties. In those cases, an iterative application ofthe BLUE method may reduce the bias of the combined measurement. The impact ofthe iterative approach compared to the standard BLUE application is studied fora wide range of possible values of uncertainties and their correlation in thecase of the combination of two measurements.