This paper considers the measurement of a quantity when a nominal value or previous estimate is available, which is the case with a quantity designed to be zero or which might be the case when a consensus value is to be calculated in a measurement comparison. If an upper bound can be placed on the magnitude of the difference between the nominal value and the true value, then the mean square error of the overall measurement procedure can be reduced by a statistical method known as shrinkage estimation. We describe the method for use in an individual measurement, but we give a deeper analysis assuming the context of a measurement comparison.
Robin Willink (Thu,) studied this question.