Defining Precision for Reliable Measurement and Estimation Procedures

The quality of a measurement or estimation procedure for the value of a parameter of interest refers to its reliability and its precision. The reliability of a measurement procedures is quantified in a straightforward way by the probability of the event of a correct measurement result. However, the quantification of the precision of a measurement procedure is not at all evident and the related problems are not satisfactorily solved so far. This paper presents and discusses several possibilities for a quantification of the measurement precision. Among others, a minmax-regret approach is introduced which takes into account the “unavoidable imprecision”. Realistically, it is assumed here that the parameter space is bounded. Moreover, it is shown how prior information can be utilized without applying the Bayesian way which considers the parameter of interest as a random variable. The theory is illustrated by the example of the measurement of the first moment of a normally distributed random variable.