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Confidence regions in singular weakly nonlinear regression models with constraints

  • Lubomír Kubáček EMAIL logo
Published/Copyright: May 2, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

It is rather complicated to construct the confidence region in nonlinear regression model mainly when number of parameters is large. If the nonlinearity of the model is weak, then it is possible, after some modification, to approximate the confidence region by a confidence ellipsoid in the linearized model. The aim of the paper is to propose a solution in singular models with constraints.

Keywords: confidence region; confidence ellipsoid; measures of nonlinearity; singularity; models with constraints; linearization region
MSC: Primary 62J05; 62F10

Supported by the Council of the Czech Government MSM 6 198 959 214.

  1. This paper has been communicated by Gejza Wimmer

[1] Fišerová, E.—KubáčEk, L.—Kunderová, P.:Linear Statistical Models; Regularity and Singularities, Academia, Praha, 2007.Search in Google Scholar

[2] KubáčEk, L.—TesaříKová, E.:Weakly Nonlinear Regression Models, Palacký University, Olomouc, 2008.Search in Google Scholar

[3] KubáčEk, L.: Linearization regions in singular weakly nonlinear regression models with constraints, Math. Slovaca 65 (2015), 1181–1198.10.1515/ms-2015-0081Search in Google Scholar

[4] Rao, C.R.—Mitra, S.K.: Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, Inc., New York-London-Sydney-Toronto, 1971.Search in Google Scholar

Received: 2012-1-9
Accepted: 2013-7-18
Published Online: 2016-5-2
Published in Print: 2016-4-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0136
Keywords for this article
confidence region; confidence ellipsoid; measures of nonlinearity; singularity; models with constraints; linearization region

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  5. Research Article
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  11. Research Article
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  13. Research Article
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