×

zbMATH — the first resource for mathematics

Linearization conditions for regression models with unknown variance parameter. (English) Zbl 1067.62547
A detailed analysis of criteria for a linearization of regression models is given. The frequently occuring situation when a variance parameter is unknown is solved. Several inequalities useful for users are found out. A test of intrinsic nonlinearity more powerful than that one used until now is also shown. The developed theory is nicely demonstrated on the Michaelis-Menten model.
MSC:
62J02 General nonlinear regression
62J05 Linear regression; mixed models
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] D. M. Bates, D. G. Watts: Relative curvature measures of nonlinearity. J. Roy. Statist. Soc. B 42 (1980), 1-25. · Zbl 0455.62028
[2] P. R. Halmos: Finite-dimensional Vector Spaces. Springer-Verlag, New York-Heidelberg-Berlin, 1974. · Zbl 0288.15002
[3] A. Jenčová: A choice of criterion parameters in linearization of regression models. Acta Math. Univ. Comenianae, Vol LXIV, 2 (1995), 227-234. · Zbl 0845.62047 · emis:journals/AMUC/_vol-64/_no_2/_jencova/jencova.html · eudml:118864
[4] L. Kubáček: On a linearization of regression models. Appl. Math. 40 (1995), 61-78. · Zbl 0819.62054 · eudml:32904
[5] L. Kubáček: Models with a low nonlinearity. Tatra Mountains Math. Publ. 7 (1996), 149-155. · Zbl 0925.62254
[6] A. Pázman: Nonlinear Statistical Models. Kluwer Acad. Publishers, Dordrecht-Boston-London, and Ister Science Press, Bratislava, 1993. · Zbl 0808.62058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.