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Keywords:
Nonlinear regression model; confidence region; singularity
Nonlinear regression model; confidence region; singularity
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 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.
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] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models, Regularity and Singularities. Academia, Praha, 2007.
[3] Kubáček, L., Kubáčková, L.: Regression models with a weak nonlinearity. Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67.
[4] Kubáček, L., Kubáčková, L.: Statistics and Metrology. Vyd. Univ. Palackého, Olomouc, 2000 (in Czech).
[5] Kubáček, L., Tesaříková, E.: Linearization region for confidence ellispoids. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 47 (2008), 101–113. MR 2482720
[6] Pázman, A.: Nonlinear Statistical Models. Kluwer Academic Publisher, Dordrecht–Boston–London and Ister Science Press, Bratislava, 1993. MR 1254661
[7] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications. J. Wiley, New York–London–Sydney–Toronto, 1971. MR 0338013 | Zbl 0236.15005
[8] Scheffé, H.: The Analysis of Variance. J. Wiley, New York–London–Sydney, 1967 (fifth printing). MR 1673563
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