In the multivariate calibration problem using a multivariate linear model, some conservative confidence regions are constructed. The regions are nonempty and invariant under nonsingular transformations. Situations where the explanatory variable occurs nonlinearly in the model are also considered. Computational aspects of the confidence region and its practical implementation are discussed. The results are illustrated using two examples. The examples show that our confidence regions are much more satisfactory compared to those based on some of the existing procedures. Furthermore, simulation results for the examples reveal that the coverage probability of the conservative confidence regions are very close to the assumed confidence level.
Thomas Mathew. Wenxing Zha. "Conservative confidence regions in multivariate calibration." Ann. Statist. 24 (2) 707 - 725, April 1996. https://doi.org/10.1214/aos/1032894461