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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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1337-2211
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Volume 66, Issue 3

Issues

Reparameterization of weakly nonlinear regression models with constraints

Lubomír Kubáček
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  • Department of Mathematical Analysis and Applications of Mathematics Faculty of Science 17. listopadu 12 771 46 Olomouc CZECH REPUBLIC
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/ Gejza Wimmer
Published Online: 2016-08-27 | DOI: https://doi.org/10.1515/ms-2015-0175

Abstract

There are several ways how to redefine the Bates and Watts curvatures in models with constraints. One of possible approaches is based on a reparametrization of models. It enables us to construct linearization regions for the bias of parameter estimators, for the confidence regions, etc., in an easy way.

Key words: nonlinear regression model; reparametrization; Bates and Watts curvatures; linearization

MSC 2010: Primary 62F10; 62J05

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

References

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    Bates, D. M.—Watts, D. G.: Relative curvature measures of nonlinearity, J. Roy. Statist. Soc. Ser. B 42 (1980), 1–25.Google Scholar

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    Fišerová, E.—Kubáček, L.—Kunderová, P.: Linear Statistical Models; Regularity and Singularities, Academia, Prague, 2007.Google Scholar

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    Kubáček, L.—Kubáčková, L.—Volaufová, J.: Statistical Models with Linear Structures, Veda, Bratislava, 1995.Google Scholar

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    Kubáček, L.—Tesaříková, E.: Weakly nonlinear regression model with constraints I: nonlinear hypothesis, Discuss. Math. Probab. Stat. 25 (2005), 115–133.Google Scholar

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    Kubáček, L.—Tesaříková, E.: Weakly Nonlinear Regression Models, Palacký University, Olomouc, 2008.Google Scholar

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    Rao, C. R.—Mitra, S. K.: Generalized Inverse of Matrices and Its Applications, J. Wiley, New York-London-Sydney-Toronto, 1971.Google Scholar

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    Scheffé, H.: The Analysis of Variance (5th ed.), J. Wiley, New York-London-Sydney, 1967.Google Scholar

About the article


Received: 2012-11-30

Accepted: 2013-11-15

Published Online: 2016-08-27

Published in Print: 2016-06-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 731–744, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0175.

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