Underparametrization of weakly nonlinear regression models
Lubomír Kubáček; Eva Tesaříková
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)
- Volume: 49, Issue: 2, page 83-93
- ISSN: 0231-9721
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topKubáček, Lubomír, and Tesaříková, Eva. "Underparametrization of weakly nonlinear regression models." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.2 (2010): 83-93. <http://eudml.org/doc/116516>.
@article{Kubáček2010,
abstract = {A large number of parameters in regression models can be serious obstacle for processing and interpretation of experimental data. One way how to overcome it is an elimination of some parameters. In some cases it need not deteriorate statistical properties of estimators of useful parameters and can help to interpret them. The problem is to find conditions which enable us to decide whether such favourable situation occurs.},
author = {Kubáček, Lubomír, Tesaříková, Eva},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Weakly nonlinear regression model; underparameterization; MSE; BLUE; MSE; BLUE},
language = {eng},
number = {2},
pages = {83-93},
publisher = {Palacký University Olomouc},
title = {Underparametrization of weakly nonlinear regression models},
url = {http://eudml.org/doc/116516},
volume = {49},
year = {2010},
}
TY - JOUR
AU - Kubáček, Lubomír
AU - Tesaříková, Eva
TI - Underparametrization of weakly nonlinear regression models
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 2
SP - 83
EP - 93
AB - A large number of parameters in regression models can be serious obstacle for processing and interpretation of experimental data. One way how to overcome it is an elimination of some parameters. In some cases it need not deteriorate statistical properties of estimators of useful parameters and can help to interpret them. The problem is to find conditions which enable us to decide whether such favourable situation occurs.
LA - eng
KW - Weakly nonlinear regression model; underparameterization; MSE; BLUE; MSE; BLUE
UR - http://eudml.org/doc/116516
ER -
References
top- Bates, D. M., Watts, D. G., Relative curvature measures of nonlinearity, J. Roy. Stat. Soc. B 42 (1980), 1–25. (1980) Zbl0455.62028MR0567196
- Kubáček, L., Kubáčková, L., Volaufová, J., Statistical Models with Linear Structures, Veda, Bratislava, 1995. (1995)
- Kubáček, L., Kubáčková, L., Regression Models with a weak Nonlinearity, Technical Report Nr. 1998.1, Universität Stuttgart, Stuttgart, 1998, 1–67. (1998)
- Kubáček, L., Underparametrization in a regression model with constraints II, Math. Slovaca 55 (2005), 579–596. (2005) Zbl1150.62390MR2200144
- Kubáček, L., Underparametrized regression models, Tatra Mt. Math. Publ. 14 (2006), 241–254. (2006)
- Kubáček, L., Tesaříková, E., Weakly Nonlinear Regression Models, Vyd. Univerzity Palackého, Olomouc, 2008. (2008)
- Rao, C. R., Mitra, S. K., Generalized Inverse of Matrices and its Applications, Wiley, New York–London–Sydney–Toronto, 1971. (1971) Zbl0236.15005MR0338013
- Scheffé, H., The Analysis of Variance, Wiley, New York–London–Sydney, 1967, (fifth printing). (1967) MR1673563
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