Comparisons of statistical calibration procedures when the standard measurement is also subject to error

Abstract

The classical theory of statistical calibration assumes that the standard measurement is free from errors. From a realistic point of view, however, this assumption needs to be relaxed so that more meaningful calibration procedures may be developed. The purpose of this thesis is to develop statistical calibration models when the standard as well as the nonstandard measurement is subject to error, and to compare relative performances of various calibration procedures. The problem of statistical calibration when both standard and nonstandard measurements are subject to error is formulated as a predictive errorsin-variables model in this thesis. Then, for the unreplicated case, the ordinary least squares and maximum likelihood estimation methods are considered to estimate the relationship between the two measurements, while for the prediction of unknown standard measurements we consider direct and inverse approaches. Relative performances of those calibration procedures are compared in terms of the asymprotic mean square error of prediction. Next, under the assumption that replicated observations are available, three estimation techniques (ordinary least squares, grouping least squares, and maximum likelihood estimation) combined with two prediction methods (direct and inverse prediction) are compared in terms of the asymptotic mean square error of prediction. Finally, a multivariate calibration problem which arises when the standard, nonstandard, and other related measurements are subject to error is presented and analyzed as an extension of the previous univariate calibration model.