Estimation of dispersion in nonlinear regression models with constraints
Lubomír Kubáček; Eva Tesaříková
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)
- Volume: 43, Issue: 1, page 75-86
- ISSN: 0231-9721
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topKubáček, Lubomír, and Tesaříková, Eva. "Estimation of dispersion in nonlinear regression models with constraints." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 75-86. <http://eudml.org/doc/32347>.
@article{Kubáček2004,
abstract = {Dispersion of measurement results is an important parameter that enables us not only to characterize not only accuracy of measurement but enables us also to construct confidence regions and to test statistical hypotheses. In nonlinear regression model the estimator of dispersion is influenced by a curvature of the manifold of the mean value of the observation vector. The aim of the paper is to find the way how to determine a tolerable level of this curvature.},
author = {Kubáček, Lubomír, Tesaříková, Eva},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {nonlinear regression model; linearization; estimation of dispersion; linearization; estimation of dispersion; measure of nonlinearity; linearization region},
language = {eng},
number = {1},
pages = {75-86},
publisher = {Palacký University Olomouc},
title = {Estimation of dispersion in nonlinear regression models with constraints},
url = {http://eudml.org/doc/32347},
volume = {43},
year = {2004},
}
TY - JOUR
AU - Kubáček, Lubomír
AU - Tesaříková, Eva
TI - Estimation of dispersion in nonlinear regression models with constraints
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 75
EP - 86
AB - Dispersion of measurement results is an important parameter that enables us not only to characterize not only accuracy of measurement but enables us also to construct confidence regions and to test statistical hypotheses. In nonlinear regression model the estimator of dispersion is influenced by a curvature of the manifold of the mean value of the observation vector. The aim of the paper is to find the way how to determine a tolerable level of this curvature.
LA - eng
KW - nonlinear regression model; linearization; estimation of dispersion; linearization; estimation of dispersion; measure of nonlinearity; linearization region
UR - http://eudml.org/doc/32347
ER -
References
top- Bates D. M., Watts D. G., Relative curvatures measures of nonlinearity, J. Roy. Statist. Soc. B 42 (1980), 1–25. (1980) MR0567196
- Kubáček L., Kubáčková L., Regression models with a weak nonlinearity, Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67. (1998)
- Kubáček L., Kubáčková L.: Statistics, Metrology., Vyd. Univ. Palackého, Olomouc, , 2000 (in Czech).
- Kubáček L., Tesaříková E., Confidence regions in nonlinear models with constraints, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 42 (2003), 43–58. Zbl1046.62065MR2056021
- Rao C. R., Mitra S. K.: Generalized Inverse of Matrices, its Applications., J. Wiley & Sons, New York–London–Sydney–Toronto, , 1971. (1971) MR0338013
- Scheffé H.: The Analysis of Variance., J. Wiley, New York, , 1959. (1959) MR0116429
- Tesaříková E., Kubáček L., Estimators of dispersion in models with constraints (demoprogram), Department of Algebra and Geometry, Faculty of Science, Palacký University, Olomouc, 2003.
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