The classical theory of statistical calibration assumes that the standard measurement is free from errors. However, in many cases, this assumption is violated, and therefore, the classical theory cannot be applied.
The purpose of this thesis is to present a statistical calibration model when not only the nonstandard, but the standard measurement is also subject to error, and to provide analysis techniques for designing the overall calibration procedures properly.
This study proposes a functional relationship model with prediction. For the analysis of the problem, two estimation techniques (ordinary least squares and grouping least squares estimation) and two prediction methods (classical and inverse prediction) are considered. The behavior of the predicted values is measured by the mean square error of prediction as well as by the probability of concentration. Asymptotic and Monte Carlo simulation results are presented and compared.
The proposed methodolgy can be used to select an appropriate estimation and predictions methods. Further, the results presented may provide guidelines for designing the calibration experiment and for developing cost-effective sampling schemes for a given situation.
