A Comparison of Multiple-Use Confidence Regions for Multivariate Calibration

Multivariate calibration problem in this paper deals with the construction of multiple use confidence regions for unknown values of an explanatory variable corresponding to a sequence of values of a multivariate normally distributed response variable, related to the explanatory variable through a multivariate linear model. It is required that at least γ of the constructed multiple use confidence regions will contain the corresponding true value of the explanatory variable with confidence 1 - α. We provide a numerical comparison of the multiple use confidence regions derived by Mathew and Zha (1997), based on the classical estimator for the unknown value of the explanatory variable, and the proposed multiple-use confidence regions constructed by inverting a tolerance region according to the confidence level and the size. Although the estimated confidence of the proposed multiple-use confidence regions is satisfactorily close to the prescribed level in our comparison study, the conservative multiple use confidence regions derived by Mathew and Zha (1997) are narrower in all considered cases in our study and we recommend them for the multivariate calibration task.