# Article

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Keywords:
confidence ellipsoid; nonlinear regression model; linearization region
Summary:
If an observation vector in a nonlinear regression model is normally distributed, then an algorithm for a determination of the exact $(1-\alpha )$-confidence region for the parameter of the mean value of the observation vector is well known. However its numerical realization is tedious and therefore it is of some interest to find some condition which enables us to construct this region in a simpler way.
References:
[1] Bates D. M., Watts D. G.: Relative curvature measures of nonlinearity. J. Roy. Stat. Soc. B 42 (1980), 1–25. MR 0567196 | Zbl 0455.62028
[2] Kubáček L., Kubáčková L., Volaufová J.: Statistical Models with Linear Structures. : Veda (Publishing House of Slovak Academy of Science), Bratislava. 1995.
[3] Kubáček L.: On a linearization of regression models. Applications of Mathematics 40 (1995), 61–78. MR 1305650
[4] Kubáček L., Kubáčková L.: Regression models with a weak nonlinearity. Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67.
[5] Kubáček L., Kubáčková L.: Statistics, Metrology. : Vyd. Univ. Palackého, Olomouc. 2000 (in Czech).
[6] Kubáček L., Tesaříková E.: Confidence regions in nonlinear models with constraints. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 42, 2003, 407–426. MR 2056021 | Zbl 1046.62065
[7] Kubáčková L.: Foundations of Experimental Data Analysis. : CRC-Press, Boca Raton-Ann Arbor–London–Tokyo. 1992. MR 1244322
[8] Pázman A.: Nonlinear Statistical Models. : Kluwer Academic Publisher, Dordrecht–Boston–London and Ister Science Press, Bratislava. 1993. MR 1254661
[10] Tesaříková E., Kubáček L.: How to deal with regression models with a weak nonlinearity. Discuss. Math., Probab. Stat. 21, 2001, 21–48. MR 1868926
[11] Tesaříková E., Kubáček L.: Estimators of dispersion in models with constraints (demoprogram). Dept. Algebra and Geometry, Fac. Sci., Palacký Univ., Olomouc, 2003.
[12] Tesaříková E., Kubáček L.: Linearization regions for confidence ellipsoids (demoprogram). Department of Algebra and Geometry, Faculty of Dept. Algebra and Geometry, Fac. Sci., Palacký Univ., Olomouc, 2007. MR 2482720

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