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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:
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