Variance components and nonlinearity

Lubomír Kubáček; Eva Tesaříková

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2006)

  • Volume: 45, Issue: 1, page 89-101
  • ISSN: 0231-9721

Abstract

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Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the paper is to contribute to a solution of the mentioned problem.

How to cite

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Kubáček, Lubomír, and Tesaříková, Eva. "Variance components and nonlinearity." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 45.1 (2006): 89-101. <http://eudml.org/doc/32513>.

@article{Kubáček2006,
abstract = {Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the paper is to contribute to a solution of the mentioned problem.},
author = {Kubáček, Lubomír, Tesaříková, Eva},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {variance components; nonlinear regression model; linearization region; insensitiveness region; linearization region; insensitiveness region},
language = {eng},
number = {1},
pages = {89-101},
publisher = {Palacký University Olomouc},
title = {Variance components and nonlinearity},
url = {http://eudml.org/doc/32513},
volume = {45},
year = {2006},
}

TY - JOUR
AU - Kubáček, Lubomír
AU - Tesaříková, Eva
TI - Variance components and nonlinearity
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2006
PB - Palacký University Olomouc
VL - 45
IS - 1
SP - 89
EP - 101
AB - Unknown parameters of the covariance matrix (variance components) of the observation vector in regression models are an unpleasant obstacle in a construction of the best estimator of the unknown parameters of the mean value of the observation vector. Estimators of variance componets must be utilized and then it is difficult to obtain the distribution of the estimators of the mean value parameters. The situation is more complicated in the case of nonlinearity of the regression model. The aim of the paper is to contribute to a solution of the mentioned problem.
LA - eng
KW - variance components; nonlinear regression model; linearization region; insensitiveness region; linearization region; insensitiveness region
UR - http://eudml.org/doc/32513
ER -

References

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  1. Bates D. M., Watts D. G., Relative curvature measures of nonlinearity, J. Roy. Stat. Soc. B 42 (1980), 1–25. (1980) Zbl0455.62028MR0567196
  2. Kubáček L., Criterion for an approximation of variance components in regression models, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 34 (1995), 91–108. (1995) MR1447258
  3. Kubáček L., Linear model with inaccurate variance components, Appl. of Math. 41, 1996, 433–445. (1996) MR1415250
  4. Kubáček L., Kubáčková L., Regression models with a weak nonlinearity, Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67. (1998) 
  5. Kubáček L., Kubáčková L., Testing statistical hypotheses in deformation measurement; one generalization of the Scheffé theorem, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 37 (1998), 81–88. (1998) Zbl0955.62061MR1690476
  6. Kubáček L., Kubáčková L.: Statistics, Metrology., Vyd. Univ. Palackého, Olomouc, , 2000 (in Czech). 
  7. Rao C. R., Mitra S. K.: Genaralized Inverse of Matrices, its Applications., John Wiley & Sons, New York– London–Sydney–Toronto, , 1971. (1971) MR0338013
  8. Rao C. R., Kleffe J.: Estimation of Variance Components, Applications., North–Holland, Amsterdam–New York–Oxford–Tokyo, , 1988. (1988) MR0933559
  9. Tesaříková E., Kubáček L., Variance componens and nonlinearity, Demoprogram, Department of Algebra and Geometry, Faculty of Science, Palacký University, Olomouc, 2005. MR2321301

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