Geodesic
Linearization regions for a confidence ellipsoid in singular nonlinear regression models
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 73-82.

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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 the 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.
Classification : 62F10, 62J05
Keywords: Nonlinear regression model; confidence region; singularity 
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Kubáček, Lubomír; Tesaříková, Eva. Linearization regions for a confidence ellipsoid in singular nonlinear regression models. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 73-82. http://geodesic.mathdoc.fr/item/AUPO_2009__48_1_a6/