What does mean mean? – A systematic treatment of statistical methods for measurand estimation

Results of a study in statistical methods for point-wise estimation are presented. Estimation criteria based on unbiasedness, minimum-mean-square-error, maximum likelihood, least squares, and on decision theory are compared and contrasted. Decision theory emerges as a parsimonious and powerful rational, able to unify both ‘frequentist’ and ‘Bayesian’ estimation principles, and to reduce inflation of ad hoc solutions.