Geodesic
Linearization regions for confidence ellipsoids
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 101-113 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 62F10, 62F25, 62J05
Keywords: confidence ellipsoid; nonlinear regression model; linearization region 
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Kubáček, Lubomír; Tesaříková, Eva. Linearization regions for confidence ellipsoids. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 47 (2008) no. 1, pp. 101-113. http://geodesic.mathdoc.fr/item/AUPO_2008_47_1_a8/

[1] Bates D. M., Watts D. G.: Relative curvature measures of nonlinearity. J. Roy. Stat. Soc. B 42 (1980), 1–25. | MR | Zbl

[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

[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 | Zbl

[7] Kubáčková L.: Foundations of Experimental Data Analysis. : CRC-Press, Boca Raton-Ann Arbor–London–Tokyo. 1992. | MR

[8] Pázman A.: Nonlinear Statistical Models. : Kluwer Academic Publisher, Dordrecht–Boston–London and Ister Science Press, Bratislava. 1993. | MR

[10] Tesaříková E., Kubáček L.: How to deal with regression models with a weak nonlinearity. Discuss. Math., Probab. Stat. 21, 2001, 21–48. | MR

[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