Conservative confidence regions in multivariate calibration. (English) Zbl 0859.62062

Summary: 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 probabilities of the conservative confidence regions are very close to the assumed confidence level.


62H99 Multivariate analysis
62F25 Parametric tolerance and confidence regions
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