We consider an estimation problem described in the Guide to the Expression of Uncertainty in Measurement (GUM). The problem is concerned with estimating a measurand that is a non-linear function of input quantities. The GUM describes two methods for estimating the measurand -- method 1 is based on the same non-linear function of input-quantity estimates and method 2 is based on the mean of that function of individual measurements. We use several examples to compare the two methods based on their mean-squared errors and to demonstrate that a uniformly preferred method may not be available except for the simplest cases. We also consider an approach based on the Monte Carlo method in Supplement 1 of the GUM for the problem and compare it with the two methods.
Pub Type: Journals
GUM, mean-squared error, ratio estimation, simulation.