| Multivariate calibration (calibration using multiple measurements per chemical sample) is becoming popular in analytical chemistry since it has several advantages over univariate calibration. They are (1) the ability to calibrate for a macroscopic property of interest in the presence of chemical species which also influence the signal. In addition, this allows for multicomponent quantitation using the output from one analytical instrument. (2) It is possible to detect the presence of an unknown chemical component in a future sample.; Implicit rather than explicit or theoretical models are often constructed, and so the models must be validated before they are used. In this dissertation methods for model validation are discussed. Multivariate calibration methods estimate a model by using least squares methods. Since the calibration data are only a small set of all possible samples, this criterion allows noise in the measurements to be incorporated into the model. A new method called parsimonious regression is presented which minimizes the prediction error, estimated by cross validation. Finally, it is shown that of two meaningful models, the most parsimonious (simplest) one is preferred when considering calibration models with minimum prediction error. The mathematical theory is used to provide a procedure for selecting the most parsimonious model structure in a given calibration application. |
