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# Article

 Title: Linearization conditions for regression models with unknown variance parameter (English) Author: Jenčová, Anna Language: English Journal: Applications of Mathematics ISSN: 0862-7940 (print) ISSN: 1572-9109 (online) Volume: 45 Issue: 2 Year: 2000 Pages: 145-160 Summary lang: English . Category: math . Summary: In the case of the nonlinear regression model, methods and procedures have been developed to obtain estimates of the parameters. These methods are much more complicated than the procedures used if the model considered is linear. Moreover, unlike the linear case, the properties of the resulting estimators are unknown and usually depend on the true values of the estimated parameters. It is sometimes possible to approximate the nonlinear model by a linear one and use the much more developed linear methods, but some procedure is needed to recognize such situations. One attempt to find such a procedure, taking into account the requirements of the user, is given in , , , where the existence of an a priori information on the parameters is assumed. Here some linearization criteria are proposed and the linearization domains, i.e. domains in the parameter space where these criteria are fulfilled, are defined. The aim of the present paper is to use a similar approach to find simple conditions for linearization of the model in the case of a locally quadratic model with unknown variance parameter $\sigma ^2$. Also a test of intrinsic nonlinearity of the model and an unbiased estimator of this parameter are derived. (English) Keyword: nonlinear regression models Keyword: linearization domains Keyword: linearization conditions MSC: 62F10 MSC: 62J02 MSC: 62J05 idZBL: Zbl 1067.62547 idMR: MR1745611 DOI: 10.1023/A:1022239613534 . Date available: 2009-09-22T18:03:07Z Last updated: 2020-07-02 Stable URL: http://hdl.handle.net/10338.dmlcz/134433 . Reference: [1] D. M. Bates, D. G.  Watts: Relative curvature measures of nonlinearity.J. Roy. Statist. Soc. B 42 (1980), 1–25. MR 0567196 Reference: [2] P. R. Halmos: Finite-dimensional Vector Spaces.Springer-Verlag, New York-Heidelberg-Berlin, 1974. Zbl 0288.15002, MR 0409503 Reference: [3] A. Jenčová: A choice of criterion parameters in linearization of regression models.Acta Math. Univ. Comenianae, Vol LXIV, 2 (1995), 227–234. MR 1391038 Reference: [4] L. Kubáček: On a linearization of regression models.Appl. Math. 40 (1995), 61–78. MR 1305650 Reference: [5] L. Kubáček: Models with a low nonlinearity.Tatra Mountains Math. Publ. 7 (1996), 149–155. MR 1408464 Reference: [6] A. Pázman: Nonlinear Statistical Models.Kluwer Acad. Publishers, Dordrecht-Boston-London, and Ister Science Press, Bratislava, 1993. MR 1254661 .

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