Linearization regions for a confidence ellipsoid in singular nonlinear regression models. (English) Zbl 1191.62119

Summary: A construction of confidence regions in nonlinear regression models is difficult mainly in the case that the dimension of an estimated vector parameter is large. A singularity is also a problem. Therefore some simple approximation of an exact confidence region is welcome. The aim of this paper is to give a small modification of a confidence ellipsoid constructed in a linearized model which is sufficient under some conditions for an approximation of the exact confidence region.


62J02 General nonlinear regression
62H12 Estimation in multivariate analysis
62F25 Parametric tolerance and confidence regions
62J05 Linear regression; mixed models


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