# Linearization conditions for regression models with unknown variance parameter

• Volume: 45, Issue: 2, page 145-160
• ISSN: 0862-7940

top

## Abstract

top
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.

## How to cite

top

Jenčová, Anna. "Linearization conditions for regression models with unknown variance parameter." Applications of Mathematics 45.2 (2000): 145-160. <http://eudml.org/doc/33053>.

@article{Jenčová2000,
abstract = {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.},
author = {Jenčová, Anna},
journal = {Applications of Mathematics},
keywords = {nonlinear regression models; linearization domains; linearization conditions; nonlinear regression models; linearization domains; linearization conditions},
language = {eng},
number = {2},
pages = {145-160},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linearization conditions for regression models with unknown variance parameter},
url = {http://eudml.org/doc/33053},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Jenčová, Anna
TI - Linearization conditions for regression models with unknown variance parameter
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 2
SP - 145
EP - 160
AB - 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.
LA - eng
KW - nonlinear regression models; linearization domains; linearization conditions; nonlinear regression models; linearization domains; linearization conditions
UR - http://eudml.org/doc/33053
ER -

## References

top
1. Relative curvature measures of nonlinearity, J. Roy. Statist. Soc. B 42 (1980), 1–25. (1980) MR0567196
2. Finite-dimensional Vector Spaces, Springer-Verlag, New York-Heidelberg-Berlin, 1974. (1974) Zbl0288.15002MR0409503
3. A choice of criterion parameters in linearization of regression models, Acta Math. Univ. Comenianae, Vol LXIV, 2 (1995), 227–234. (1995) MR1391038
4. On a linearization of regression models, Appl. Math. 40 (1995), 61–78. (1995) MR1305650
5. Models with a low nonlinearity, Tatra Mountains Math. Publ. 7 (1996), 149–155. (1996) MR1408464
6. Nonlinear Statistical Models, Kluwer Acad. Publishers, Dordrecht-Boston-London, and Ister Science Press, Bratislava, 1993. (1993) MR1254661

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.