Geodesic
Variance components and nonlinearity
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 89-101 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 62F10, 62H12, 62J02, 62J05, 62N02
Keywords: variance components; nonlinear regression model; linearization region; insensitiveness region 
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Kubáček, Lubomír; Tesaříková, Eva. Variance components and nonlinearity. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 45 (2006) no. 1, pp. 89-101. http://geodesic.mathdoc.fr/item/AUPO_2006_45_1_a8/

[1] Bates D. M., Watts D. G.: Relative curvature measures of nonlinearity. J. Roy. Stat. Soc. B 42 (1980), 1–25. | MR | Zbl

[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. | MR

[3] Kubáček L.: Linear model with inaccurate variance components. Appl. of Math. 41, 1996, 433–445. | MR

[4] Kubáček L., Kubáčková L.: Regression models with a weak nonlinearity. Technical report Nr. 1998.1, Universität Stuttgart, 1998, 1–67.

[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. | MR | Zbl

[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. | MR

[8] Rao C. R., Kleffe J.: Estimation of Variance Components, Applications. : North–Holland, Amsterdam–New York–Oxford–Tokyo. 1988. | MR

[9] Tesaříková E., Kubáček L.: Variance componens and nonlinearity. Demoprogram, Department of Algebra and Geometry, Faculty of Science, Palacký University, Olomouc, 2005. | MR