Title: Multiple-use confidence regions in multivariate calibration problem
Authors: Martina Chvostekova - Institute of Measurement Science, Slovak Academy of Sciences (Slovakia) [presenting]
Abstract: The problem of statistical multivariate calibration is considered in the setup where a normally distributed response variable is related to an explanatory variable through a multivariate linear regression model. The statistical multivariate calibration problem consists of constructing region estimates for future unobserved values of $m$-dimensional explanatory variable corresponding to possibly infinitely many future observations of $q$-dimensional response variable by repeatedly using a calibration data from a calibration experiment. The region estimates are referred as multiple-use confidence regions. It is required that at least $\gamma$ proportion of the constructed multiple-use confidence regions after observing a sequence of future responses will contain the corresponding true value of an explanatory variable. Since the multiple-use confidence regions are derived using the same calibration data, the probability of a $\gamma$ coverage is $1 - \alpha$. We present a procedure for determining the multiple-use confidence regions employing the tolerance regions. The provided numerical investigation shows that the regions so obtained satisfy the coverage requirements quite well. The computational aspects and the practical implementation of our multiple-use confidence regions and those previously published are illustrated using an example.